QBManager

Dual nature of radiation and Matter

142612 The energy of a photon of light with wavelength $5000 \AA$ is approximately $2.5 eV$ . This way the energy of an X-ray photon with wavelength $1 \AA$ would be

1

\frac{2.5}{(5000)^{2}} cV

2

2.5 \times 5000 eV

3

\frac{2.5}{(5000)^{2}} eV

4

\frac{2.5}{5000} eV

Explanation:

B Given,
Wavelength $(λ_{1}) = 5000 \AA$ , Energy $(E_{1}) = 2.5 eV$
When wavelength $(λ_{2}) = 1 \AA$ , Energy $(E_{2}) =$ ?
We know that,
$E = \frac{hc}{λ}$
$E \propto \frac{1}{λ} (∵ h & c have constant value)$
$\frac{E_{1}}{E_{2}} = \frac{λ_{2}}{λ .1}$
$\frac{2.5}{E_{2}} = \frac{1}{5000}$
$E_{2} = 2.5 \times 5000 eV$

AIIMS-2010

Dual nature of radiation and Matter

142613 Hard X-rays for the study of fractures in bones should have a minimum wavelength of $10^{11} m$ . The accelerating voltage for electrons in $X$ -ray machine should be

1

< 124.2 kV

2

> 124.2 kV

3 Between

60 kV

and

70 kV

4

λ_{min} = 10^{- 11} m

Explanation:

A Given,
We know that,
$λ_{min} = \frac{hc}{eV}$
$V = \frac{hc}{λ_{min} e}$
$V = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{10^{- 11} \times 1.6 \times 10^{- 19}}$
$V = 123.75 kV$
$123.75 kV < 124.2 kV$

Dual nature of radiation and Matter

142617 The frequencies of $X$ rays, $Y$ rays and Ultra violet rays are respectively $p, q$ and $r$ then

1 p

>

q, q

<

r

2 p

>

q, q

>

r

3 p

<

q, q

<

r

4 p

<

q, q

>

r

Explanation:

D Given,
Frequencies of $X$ -rays $= p$
Frequencies of $γ -$ rays $= q$
Frequencies of ultraviolet rays $= r$
We know,
$p = 10^{17} to 10^{20} Hz$
$q = 10^{20} to 10^{24} Hz$
$r = 10^{15} to 10^{17} Hz$
Hence, $q > p$ and $q > r$

GUJCET 2016

Dual nature of radiation and Matter

142618 X-ray of wavelength $λ = 2 \AA$ is emitted from the target metal. The potential difference applied across the cathode and the metal target is

1

6200 V

2

2000 V

3

7000 V

4

3500 V

Explanation:

A Given that,
$λ = 2 \hat{A} = 2 \times 10^{- 10} m$
$h = 6.62 \times 10^{- 34} J - s$
$c = 3 \times 10^{8} m / s$
Energy of X-ray emitted -
$E = \frac{hc}{λ}$
$V_{o} = \frac{hc}{λ e}$
$V_{o} = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8}}{2 \times 10^{- 10} \times 1.6 \times 10^{- 19}}$
$V_{o} = 6.200 \times 10^{3}$
$V_{o} = 6200 V$

COMEDK 2016

Dual nature of radiation and Matter

142612 The energy of a photon of light with wavelength $5000 \AA$ is approximately $2.5 eV$ . This way the energy of an X-ray photon with wavelength $1 \AA$ would be

1

\frac{2.5}{(5000)^{2}} cV

2

2.5 \times 5000 eV

3

\frac{2.5}{(5000)^{2}} eV

4

\frac{2.5}{5000} eV

Explanation:

B Given,
Wavelength $(λ_{1}) = 5000 \AA$ , Energy $(E_{1}) = 2.5 eV$
When wavelength $(λ_{2}) = 1 \AA$ , Energy $(E_{2}) =$ ?
We know that,
$E = \frac{hc}{λ}$
$E \propto \frac{1}{λ} (∵ h & c have constant value)$
$\frac{E_{1}}{E_{2}} = \frac{λ_{2}}{λ .1}$
$\frac{2.5}{E_{2}} = \frac{1}{5000}$
$E_{2} = 2.5 \times 5000 eV$

AIIMS-2010

Dual nature of radiation and Matter

142613 Hard X-rays for the study of fractures in bones should have a minimum wavelength of $10^{11} m$ . The accelerating voltage for electrons in $X$ -ray machine should be

1

< 124.2 kV

2

> 124.2 kV

3 Between

60 kV

and

70 kV

4

λ_{min} = 10^{- 11} m

Explanation:

A Given,
We know that,
$λ_{min} = \frac{hc}{eV}$
$V = \frac{hc}{λ_{min} e}$
$V = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{10^{- 11} \times 1.6 \times 10^{- 19}}$
$V = 123.75 kV$
$123.75 kV < 124.2 kV$

Dual nature of radiation and Matter

142617 The frequencies of $X$ rays, $Y$ rays and Ultra violet rays are respectively $p, q$ and $r$ then

1 p

>

q, q

<

r

2 p

>

q, q

>

r

3 p

<

q, q

<

r

4 p

<

q, q

>

r

Explanation:

D Given,
Frequencies of $X$ -rays $= p$
Frequencies of $γ -$ rays $= q$
Frequencies of ultraviolet rays $= r$
We know,
$p = 10^{17} to 10^{20} Hz$
$q = 10^{20} to 10^{24} Hz$
$r = 10^{15} to 10^{17} Hz$
Hence, $q > p$ and $q > r$

GUJCET 2016

Dual nature of radiation and Matter

142618 X-ray of wavelength $λ = 2 \AA$ is emitted from the target metal. The potential difference applied across the cathode and the metal target is

1

6200 V

2

2000 V

3

7000 V

4

3500 V

Explanation:

A Given that,
$λ = 2 \hat{A} = 2 \times 10^{- 10} m$
$h = 6.62 \times 10^{- 34} J - s$
$c = 3 \times 10^{8} m / s$
Energy of X-ray emitted -
$E = \frac{hc}{λ}$
$V_{o} = \frac{hc}{λ e}$
$V_{o} = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8}}{2 \times 10^{- 10} \times 1.6 \times 10^{- 19}}$
$V_{o} = 6.200 \times 10^{3}$
$V_{o} = 6200 V$

COMEDK 2016

Dual nature of radiation and Matter

142612 The energy of a photon of light with wavelength $5000 \AA$ is approximately $2.5 eV$ . This way the energy of an X-ray photon with wavelength $1 \AA$ would be

1

\frac{2.5}{(5000)^{2}} cV

2

2.5 \times 5000 eV

3

\frac{2.5}{(5000)^{2}} eV

4

\frac{2.5}{5000} eV

Explanation:

B Given,
Wavelength $(λ_{1}) = 5000 \AA$ , Energy $(E_{1}) = 2.5 eV$
When wavelength $(λ_{2}) = 1 \AA$ , Energy $(E_{2}) =$ ?
We know that,
$E = \frac{hc}{λ}$
$E \propto \frac{1}{λ} (∵ h & c have constant value)$
$\frac{E_{1}}{E_{2}} = \frac{λ_{2}}{λ .1}$
$\frac{2.5}{E_{2}} = \frac{1}{5000}$
$E_{2} = 2.5 \times 5000 eV$

AIIMS-2010

Dual nature of radiation and Matter

142613 Hard X-rays for the study of fractures in bones should have a minimum wavelength of $10^{11} m$ . The accelerating voltage for electrons in $X$ -ray machine should be

1

< 124.2 kV

2

> 124.2 kV

3 Between

60 kV

and

70 kV

4

λ_{min} = 10^{- 11} m

Explanation:

A Given,
We know that,
$λ_{min} = \frac{hc}{eV}$
$V = \frac{hc}{λ_{min} e}$
$V = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{10^{- 11} \times 1.6 \times 10^{- 19}}$
$V = 123.75 kV$
$123.75 kV < 124.2 kV$

Dual nature of radiation and Matter

142617 The frequencies of $X$ rays, $Y$ rays and Ultra violet rays are respectively $p, q$ and $r$ then

1 p

>

q, q

<

r

2 p

>

q, q

>

r

3 p

<

q, q

<

r

4 p

<

q, q

>

r

Explanation:

D Given,
Frequencies of $X$ -rays $= p$
Frequencies of $γ -$ rays $= q$
Frequencies of ultraviolet rays $= r$
We know,
$p = 10^{17} to 10^{20} Hz$
$q = 10^{20} to 10^{24} Hz$
$r = 10^{15} to 10^{17} Hz$
Hence, $q > p$ and $q > r$

GUJCET 2016

Dual nature of radiation and Matter

142618 X-ray of wavelength $λ = 2 \AA$ is emitted from the target metal. The potential difference applied across the cathode and the metal target is

1

6200 V

2

2000 V

3

7000 V

4

3500 V

Explanation:

A Given that,
$λ = 2 \hat{A} = 2 \times 10^{- 10} m$
$h = 6.62 \times 10^{- 34} J - s$
$c = 3 \times 10^{8} m / s$
Energy of X-ray emitted -
$E = \frac{hc}{λ}$
$V_{o} = \frac{hc}{λ e}$
$V_{o} = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8}}{2 \times 10^{- 10} \times 1.6 \times 10^{- 19}}$
$V_{o} = 6.200 \times 10^{3}$
$V_{o} = 6200 V$

COMEDK 2016

Dual nature of radiation and Matter

142612 The energy of a photon of light with wavelength $5000 \AA$ is approximately $2.5 eV$ . This way the energy of an X-ray photon with wavelength $1 \AA$ would be

1

\frac{2.5}{(5000)^{2}} cV

2

2.5 \times 5000 eV

3

\frac{2.5}{(5000)^{2}} eV

4

\frac{2.5}{5000} eV

Explanation:

B Given,
Wavelength $(λ_{1}) = 5000 \AA$ , Energy $(E_{1}) = 2.5 eV$
When wavelength $(λ_{2}) = 1 \AA$ , Energy $(E_{2}) =$ ?
We know that,
$E = \frac{hc}{λ}$
$E \propto \frac{1}{λ} (∵ h & c have constant value)$
$\frac{E_{1}}{E_{2}} = \frac{λ_{2}}{λ .1}$
$\frac{2.5}{E_{2}} = \frac{1}{5000}$
$E_{2} = 2.5 \times 5000 eV$

AIIMS-2010

Dual nature of radiation and Matter

142613 Hard X-rays for the study of fractures in bones should have a minimum wavelength of $10^{11} m$ . The accelerating voltage for electrons in $X$ -ray machine should be

1

< 124.2 kV

2

> 124.2 kV

3 Between

60 kV

and

70 kV

4

λ_{min} = 10^{- 11} m

Explanation:

A Given,
We know that,
$λ_{min} = \frac{hc}{eV}$
$V = \frac{hc}{λ_{min} e}$
$V = \frac{6.6 \times 10^{- 34} \times 3 \times 10^{8}}{10^{- 11} \times 1.6 \times 10^{- 19}}$
$V = 123.75 kV$
$123.75 kV < 124.2 kV$

Dual nature of radiation and Matter

142617 The frequencies of $X$ rays, $Y$ rays and Ultra violet rays are respectively $p, q$ and $r$ then

1 p

>

q, q

<

r

2 p

>

q, q

>

r

3 p

<

q, q

<

r

4 p

<

q, q

>

r

Explanation:

D Given,
Frequencies of $X$ -rays $= p$
Frequencies of $γ -$ rays $= q$
Frequencies of ultraviolet rays $= r$
We know,
$p = 10^{17} to 10^{20} Hz$
$q = 10^{20} to 10^{24} Hz$
$r = 10^{15} to 10^{17} Hz$
Hence, $q > p$ and $q > r$

GUJCET 2016

Dual nature of radiation and Matter

142618 X-ray of wavelength $λ = 2 \AA$ is emitted from the target metal. The potential difference applied across the cathode and the metal target is

1

6200 V

2

2000 V

3

7000 V

4

3500 V

Explanation:

A Given that,
$λ = 2 \hat{A} = 2 \times 10^{- 10} m$
$h = 6.62 \times 10^{- 34} J - s$
$c = 3 \times 10^{8} m / s$
Energy of X-ray emitted -
$E = \frac{hc}{λ}$
$V_{o} = \frac{hc}{λ e}$
$V_{o} = \frac{6.62 \times 10^{- 34} \times 3 \times 10^{8}}{2 \times 10^{- 10} \times 1.6 \times 10^{- 19}}$
$V_{o} = 6.200 \times 10^{3}$
$V_{o} = 6200 V$

COMEDK 2016

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