QBManager

Dual nature of radiation and Matter

142605 When two different material $A$ and $B$ having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in coolidge $γ$ -ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.

The correct relation is

1

V_{1} > V_{2}

and

Z_{1} > Z_{2}

2

V_{1} < V_{2}

and

Z_{1} < Z_{2}

3

V_{1} < V_{2}

and

Z_{1} > Z_{2}

4

V_{1} > V_{2}

and

Z_{1} < Z_{2}

Explanation:

D
For continuous portion
$E = \frac{hc}{λ}$
$eV = \frac{hc}{λ}$
$V \propto \frac{1}{λ}$
$(∵ E - eV)$
From the graph
$λ_{2} > λ_{1} then V_{1} > V_{2}$
For characteristic portion
From Moselly's law characteristic
$\sqrt{f} = a (Z - b)$
$f = (a (Z - b))^{2}$
$f \propto (Z - 1)^{2}$
$λ \propto \frac{1}{(Z - 1)^{2}}$
$(∵ f \propto \frac{1}{λ})$
$λ_{1} > λ_{2}$ then $Z_{2} > Z_{1}$

CG PET- 2008

Dual nature of radiation and Matter

142606 An $X =$ ray tube operates on $30 KV$ . What is the minimum wavelength emitted?
$(h = 6.6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}, e = 1.6 \times 10^{- 19} C)$

1

0.133 \AA

2

0.4 \AA

3

1.2 A

4

6.6 \AA

Explanation:

B Given,
Voltage $(V) = 30 kV = 30 \times 10^{3} V$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light (c) $= 3 \times 10^{8} m / s$
Charge on electron (e) $= 1.6 \times 10^{- 19} C$
We know that,
$λ_{min} = \frac{h c}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 30 \times 10^{3}}$
$λ_{min} = 0.4125 \times 10^{- 10}$
$λ_{min} = 0.4 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142607 The wavelength of the most energetic $X$ -ray emitted when a metal target is bombarded by $100 keV$ electrons is approximately.

1

12 \AA

2

4 \AA

3

0.31 \AA

4

0.124 \AA

Explanation:

D Given,
Voltage $(V) = 100 keV = 100 \times 10^{3} \times 1.6 \times 10^{- 19}$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light $(c) = 3 \times 10^{8} m / s$
We know that,
$λ = \frac{hc}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 100 \times 10^{3}}$
$λ = 0.12375 \times 10^{- 10} m$
$λ = 0.124 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142609 If the frequency of $k_{α}, X$ -ray of the element of atomic number 31 is $f$ , then the frequency of $k_{α}$ , $X$ -ray for atomic number $51$ is

1

25 / 9 f

2

16 / 25 f

3

9 / 25 f

4 zero

Explanation:

A Given,
Atomic $Number (Z_{1}) = 31$ and frequency $(f_{1}) = f$ Atomomic Number $(Z_{2}) = 51$ then frequency $(f_{2}) =$ ?
We know,
$f \propto (Z - 1)^{2}$
$\frac{f_{1}}{f_{2}} = {(\frac{Z_{1} - 1}{Z_{2} - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{31 - 1}{51 - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{30}{50})}^{2}$
$f_{2} = \frac{25}{9} f$

CG PET- 2006

Dual nature of radiation and Matter

142611 Assertion: Soft and hard X-rays differ in frequency as well as velocity.
Reason: The penetrating power of hard $X$ -rays is more than the penetrating power of soft X-rays.

1 If both Assertion and Reason are correct and reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3 If Assertion is correct but Reason is incorrect

4 If both the Assertion and Reason are incorrect

Explanation:

B There are two types of X-rays, according to their photon energy.
The photon energy given by,
$E = h v$
Where, $E =$ Energy in Joule
$h =$ Plank's constant
$v =$ frequency
Soft X-rays have low photon energy, longer wavelength, low frequency, and low penetrating power. Hard X-rays have high photon energy, shorter wavelength, high frequency and more penetrating power than soft X-rays.

AIIMS-2010

Dual nature of radiation and Matter

142605 When two different material $A$ and $B$ having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in coolidge $γ$ -ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.

The correct relation is

1

V_{1} > V_{2}

and

Z_{1} > Z_{2}

2

V_{1} < V_{2}

and

Z_{1} < Z_{2}

3

V_{1} < V_{2}

and

Z_{1} > Z_{2}

4

V_{1} > V_{2}

and

Z_{1} < Z_{2}

Explanation:

D
For continuous portion
$E = \frac{hc}{λ}$
$eV = \frac{hc}{λ}$
$V \propto \frac{1}{λ}$
$(∵ E - eV)$
From the graph
$λ_{2} > λ_{1} then V_{1} > V_{2}$
For characteristic portion
From Moselly's law characteristic
$\sqrt{f} = a (Z - b)$
$f = (a (Z - b))^{2}$
$f \propto (Z - 1)^{2}$
$λ \propto \frac{1}{(Z - 1)^{2}}$
$(∵ f \propto \frac{1}{λ})$
$λ_{1} > λ_{2}$ then $Z_{2} > Z_{1}$

CG PET- 2008

Dual nature of radiation and Matter

142606 An $X =$ ray tube operates on $30 KV$ . What is the minimum wavelength emitted?
$(h = 6.6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}, e = 1.6 \times 10^{- 19} C)$

1

0.133 \AA

2

0.4 \AA

3

1.2 A

4

6.6 \AA

Explanation:

B Given,
Voltage $(V) = 30 kV = 30 \times 10^{3} V$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light (c) $= 3 \times 10^{8} m / s$
Charge on electron (e) $= 1.6 \times 10^{- 19} C$
We know that,
$λ_{min} = \frac{h c}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 30 \times 10^{3}}$
$λ_{min} = 0.4125 \times 10^{- 10}$
$λ_{min} = 0.4 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142607 The wavelength of the most energetic $X$ -ray emitted when a metal target is bombarded by $100 keV$ electrons is approximately.

1

12 \AA

2

4 \AA

3

0.31 \AA

4

0.124 \AA

Explanation:

D Given,
Voltage $(V) = 100 keV = 100 \times 10^{3} \times 1.6 \times 10^{- 19}$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light $(c) = 3 \times 10^{8} m / s$
We know that,
$λ = \frac{hc}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 100 \times 10^{3}}$
$λ = 0.12375 \times 10^{- 10} m$
$λ = 0.124 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142609 If the frequency of $k_{α}, X$ -ray of the element of atomic number 31 is $f$ , then the frequency of $k_{α}$ , $X$ -ray for atomic number $51$ is

1

25 / 9 f

2

16 / 25 f

3

9 / 25 f

4 zero

Explanation:

A Given,
Atomic $Number (Z_{1}) = 31$ and frequency $(f_{1}) = f$ Atomomic Number $(Z_{2}) = 51$ then frequency $(f_{2}) =$ ?
We know,
$f \propto (Z - 1)^{2}$
$\frac{f_{1}}{f_{2}} = {(\frac{Z_{1} - 1}{Z_{2} - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{31 - 1}{51 - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{30}{50})}^{2}$
$f_{2} = \frac{25}{9} f$

CG PET- 2006

Dual nature of radiation and Matter

142611 Assertion: Soft and hard X-rays differ in frequency as well as velocity.
Reason: The penetrating power of hard $X$ -rays is more than the penetrating power of soft X-rays.

1 If both Assertion and Reason are correct and reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3 If Assertion is correct but Reason is incorrect

4 If both the Assertion and Reason are incorrect

Explanation:

B There are two types of X-rays, according to their photon energy.
The photon energy given by,
$E = h v$
Where, $E =$ Energy in Joule
$h =$ Plank's constant
$v =$ frequency
Soft X-rays have low photon energy, longer wavelength, low frequency, and low penetrating power. Hard X-rays have high photon energy, shorter wavelength, high frequency and more penetrating power than soft X-rays.

AIIMS-2010

Dual nature of radiation and Matter

142605 When two different material $A$ and $B$ having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in coolidge $γ$ -ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.

The correct relation is

1

V_{1} > V_{2}

and

Z_{1} > Z_{2}

2

V_{1} < V_{2}

and

Z_{1} < Z_{2}

3

V_{1} < V_{2}

and

Z_{1} > Z_{2}

4

V_{1} > V_{2}

and

Z_{1} < Z_{2}

Explanation:

D
For continuous portion
$E = \frac{hc}{λ}$
$eV = \frac{hc}{λ}$
$V \propto \frac{1}{λ}$
$(∵ E - eV)$
From the graph
$λ_{2} > λ_{1} then V_{1} > V_{2}$
For characteristic portion
From Moselly's law characteristic
$\sqrt{f} = a (Z - b)$
$f = (a (Z - b))^{2}$
$f \propto (Z - 1)^{2}$
$λ \propto \frac{1}{(Z - 1)^{2}}$
$(∵ f \propto \frac{1}{λ})$
$λ_{1} > λ_{2}$ then $Z_{2} > Z_{1}$

CG PET- 2008

Dual nature of radiation and Matter

142606 An $X =$ ray tube operates on $30 KV$ . What is the minimum wavelength emitted?
$(h = 6.6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}, e = 1.6 \times 10^{- 19} C)$

1

0.133 \AA

2

0.4 \AA

3

1.2 A

4

6.6 \AA

Explanation:

B Given,
Voltage $(V) = 30 kV = 30 \times 10^{3} V$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light (c) $= 3 \times 10^{8} m / s$
Charge on electron (e) $= 1.6 \times 10^{- 19} C$
We know that,
$λ_{min} = \frac{h c}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 30 \times 10^{3}}$
$λ_{min} = 0.4125 \times 10^{- 10}$
$λ_{min} = 0.4 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142607 The wavelength of the most energetic $X$ -ray emitted when a metal target is bombarded by $100 keV$ electrons is approximately.

1

12 \AA

2

4 \AA

3

0.31 \AA

4

0.124 \AA

Explanation:

D Given,
Voltage $(V) = 100 keV = 100 \times 10^{3} \times 1.6 \times 10^{- 19}$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light $(c) = 3 \times 10^{8} m / s$
We know that,
$λ = \frac{hc}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 100 \times 10^{3}}$
$λ = 0.12375 \times 10^{- 10} m$
$λ = 0.124 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142609 If the frequency of $k_{α}, X$ -ray of the element of atomic number 31 is $f$ , then the frequency of $k_{α}$ , $X$ -ray for atomic number $51$ is

1

25 / 9 f

2

16 / 25 f

3

9 / 25 f

4 zero

Explanation:

A Given,
Atomic $Number (Z_{1}) = 31$ and frequency $(f_{1}) = f$ Atomomic Number $(Z_{2}) = 51$ then frequency $(f_{2}) =$ ?
We know,
$f \propto (Z - 1)^{2}$
$\frac{f_{1}}{f_{2}} = {(\frac{Z_{1} - 1}{Z_{2} - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{31 - 1}{51 - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{30}{50})}^{2}$
$f_{2} = \frac{25}{9} f$

CG PET- 2006

Dual nature of radiation and Matter

142611 Assertion: Soft and hard X-rays differ in frequency as well as velocity.
Reason: The penetrating power of hard $X$ -rays is more than the penetrating power of soft X-rays.

1 If both Assertion and Reason are correct and reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3 If Assertion is correct but Reason is incorrect

4 If both the Assertion and Reason are incorrect

Explanation:

B There are two types of X-rays, according to their photon energy.
The photon energy given by,
$E = h v$
Where, $E =$ Energy in Joule
$h =$ Plank's constant
$v =$ frequency
Soft X-rays have low photon energy, longer wavelength, low frequency, and low penetrating power. Hard X-rays have high photon energy, shorter wavelength, high frequency and more penetrating power than soft X-rays.

AIIMS-2010

Dual nature of radiation and Matter

142605 When two different material $A$ and $B$ having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in coolidge $γ$ -ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.

The correct relation is

1

V_{1} > V_{2}

and

Z_{1} > Z_{2}

2

V_{1} < V_{2}

and

Z_{1} < Z_{2}

3

V_{1} < V_{2}

and

Z_{1} > Z_{2}

4

V_{1} > V_{2}

and

Z_{1} < Z_{2}

Explanation:

D
For continuous portion
$E = \frac{hc}{λ}$
$eV = \frac{hc}{λ}$
$V \propto \frac{1}{λ}$
$(∵ E - eV)$
From the graph
$λ_{2} > λ_{1} then V_{1} > V_{2}$
For characteristic portion
From Moselly's law characteristic
$\sqrt{f} = a (Z - b)$
$f = (a (Z - b))^{2}$
$f \propto (Z - 1)^{2}$
$λ \propto \frac{1}{(Z - 1)^{2}}$
$(∵ f \propto \frac{1}{λ})$
$λ_{1} > λ_{2}$ then $Z_{2} > Z_{1}$

CG PET- 2008

Dual nature of radiation and Matter

142606 An $X =$ ray tube operates on $30 KV$ . What is the minimum wavelength emitted?
$(h = 6.6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}, e = 1.6 \times 10^{- 19} C)$

1

0.133 \AA

2

0.4 \AA

3

1.2 A

4

6.6 \AA

Explanation:

B Given,
Voltage $(V) = 30 kV = 30 \times 10^{3} V$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light (c) $= 3 \times 10^{8} m / s$
Charge on electron (e) $= 1.6 \times 10^{- 19} C$
We know that,
$λ_{min} = \frac{h c}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 30 \times 10^{3}}$
$λ_{min} = 0.4125 \times 10^{- 10}$
$λ_{min} = 0.4 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142607 The wavelength of the most energetic $X$ -ray emitted when a metal target is bombarded by $100 keV$ electrons is approximately.

1

12 \AA

2

4 \AA

3

0.31 \AA

4

0.124 \AA

Explanation:

D Given,
Voltage $(V) = 100 keV = 100 \times 10^{3} \times 1.6 \times 10^{- 19}$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light $(c) = 3 \times 10^{8} m / s$
We know that,
$λ = \frac{hc}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 100 \times 10^{3}}$
$λ = 0.12375 \times 10^{- 10} m$
$λ = 0.124 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142609 If the frequency of $k_{α}, X$ -ray of the element of atomic number 31 is $f$ , then the frequency of $k_{α}$ , $X$ -ray for atomic number $51$ is

1

25 / 9 f

2

16 / 25 f

3

9 / 25 f

4 zero

Explanation:

A Given,
Atomic $Number (Z_{1}) = 31$ and frequency $(f_{1}) = f$ Atomomic Number $(Z_{2}) = 51$ then frequency $(f_{2}) =$ ?
We know,
$f \propto (Z - 1)^{2}$
$\frac{f_{1}}{f_{2}} = {(\frac{Z_{1} - 1}{Z_{2} - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{31 - 1}{51 - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{30}{50})}^{2}$
$f_{2} = \frac{25}{9} f$

CG PET- 2006

Dual nature of radiation and Matter

142611 Assertion: Soft and hard X-rays differ in frequency as well as velocity.
Reason: The penetrating power of hard $X$ -rays is more than the penetrating power of soft X-rays.

1 If both Assertion and Reason are correct and reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3 If Assertion is correct but Reason is incorrect

4 If both the Assertion and Reason are incorrect

Explanation:

B There are two types of X-rays, according to their photon energy.
The photon energy given by,
$E = h v$
Where, $E =$ Energy in Joule
$h =$ Plank's constant
$v =$ frequency
Soft X-rays have low photon energy, longer wavelength, low frequency, and low penetrating power. Hard X-rays have high photon energy, shorter wavelength, high frequency and more penetrating power than soft X-rays.

AIIMS-2010

Dual nature of radiation and Matter

142605 When two different material $A$ and $B$ having atomic number $Z_{1}$ and $Z_{2}$ are used as the target in coolidge $γ$ -ray tube at different operating voltage $V_{1}$ and $V_{2}$ respectively their spectrums are found as below.

The correct relation is

1

V_{1} > V_{2}

and

Z_{1} > Z_{2}

2

V_{1} < V_{2}

and

Z_{1} < Z_{2}

3

V_{1} < V_{2}

and

Z_{1} > Z_{2}

4

V_{1} > V_{2}

and

Z_{1} < Z_{2}

Explanation:

D
For continuous portion
$E = \frac{hc}{λ}$
$eV = \frac{hc}{λ}$
$V \propto \frac{1}{λ}$
$(∵ E - eV)$
From the graph
$λ_{2} > λ_{1} then V_{1} > V_{2}$
For characteristic portion
From Moselly's law characteristic
$\sqrt{f} = a (Z - b)$
$f = (a (Z - b))^{2}$
$f \propto (Z - 1)^{2}$
$λ \propto \frac{1}{(Z - 1)^{2}}$
$(∵ f \propto \frac{1}{λ})$
$λ_{1} > λ_{2}$ then $Z_{2} > Z_{1}$

CG PET- 2008

Dual nature of radiation and Matter

142606 An $X =$ ray tube operates on $30 KV$ . What is the minimum wavelength emitted?
$(h = 6.6 \times 10^{- 34} Js, c = 3 \times 10^{8} {ms}^{- 1}, e = 1.6 \times 10^{- 19} C)$

1

0.133 \AA

2

0.4 \AA

3

1.2 A

4

6.6 \AA

Explanation:

B Given,
Voltage $(V) = 30 kV = 30 \times 10^{3} V$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light (c) $= 3 \times 10^{8} m / s$
Charge on electron (e) $= 1.6 \times 10^{- 19} C$
We know that,
$λ_{min} = \frac{h c}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 30 \times 10^{3}}$
$λ_{min} = 0.4125 \times 10^{- 10}$
$λ_{min} = 0.4 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142607 The wavelength of the most energetic $X$ -ray emitted when a metal target is bombarded by $100 keV$ electrons is approximately.

1

12 \AA

2

4 \AA

3

0.31 \AA

4

0.124 \AA

Explanation:

D Given,
Voltage $(V) = 100 keV = 100 \times 10^{3} \times 1.6 \times 10^{- 19}$
Planck's constant $(h) = 6.6 \times 10^{- 34} J - s$
Speed of light $(c) = 3 \times 10^{8} m / s$
We know that,
$λ = \frac{hc}{eV} = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{1.6 \times 10^{- 19} \times 100 \times 10^{3}}$
$λ = 0.12375 \times 10^{- 10} m$
$λ = 0.124 \AA$

CG PET- 2007

Dual nature of radiation and Matter

142609 If the frequency of $k_{α}, X$ -ray of the element of atomic number 31 is $f$ , then the frequency of $k_{α}$ , $X$ -ray for atomic number $51$ is

1

25 / 9 f

2

16 / 25 f

3

9 / 25 f

4 zero

Explanation:

A Given,
Atomic $Number (Z_{1}) = 31$ and frequency $(f_{1}) = f$ Atomomic Number $(Z_{2}) = 51$ then frequency $(f_{2}) =$ ?
We know,
$f \propto (Z - 1)^{2}$
$\frac{f_{1}}{f_{2}} = {(\frac{Z_{1} - 1}{Z_{2} - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{31 - 1}{51 - 1})}^{2}$
$\frac{f}{f_{2}} = {(\frac{30}{50})}^{2}$
$f_{2} = \frac{25}{9} f$

CG PET- 2006

Dual nature of radiation and Matter

142611 Assertion: Soft and hard X-rays differ in frequency as well as velocity.
Reason: The penetrating power of hard $X$ -rays is more than the penetrating power of soft X-rays.

1 If both Assertion and Reason are correct and reason is the correct explanation of Assertion.

2 If both Assertion and Reason are correct, but Reason is not the correct explanation of Assertion

3 If Assertion is correct but Reason is incorrect

4 If both the Assertion and Reason are incorrect

Explanation:

B There are two types of X-rays, according to their photon energy.
The photon energy given by,
$E = h v$
Where, $E =$ Energy in Joule
$h =$ Plank's constant
$v =$ frequency
Soft X-rays have low photon energy, longer wavelength, low frequency, and low penetrating power. Hard X-rays have high photon energy, shorter wavelength, high frequency and more penetrating power than soft X-rays.

AIIMS-2010

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