145279
The radius of hydrogen atom in its ground state is $5.3 \times 10^{-11} \mathrm{~m}$. After collision with an electron it is found to have a radius of $21.2 \times$ $10^{-11} \mathrm{~m}$. What is the principal quantum number $n$ of the final state of atom ?
1 $\mathrm{n}=4$
2 $n=2$
3 $\mathrm{n}=16$
4 $\mathrm{n}=3$
Explanation:
B Given, Radius of ground state $\left(\mathrm{r}_{1}\right)=5.3 \times 10^{-11} \mathrm{~m}$ Radius of $\mathrm{n}^{\text {th }}$ state $\left(\mathrm{r}_{2}\right)=21.2 \times 10^{-11} \mathrm{~m}$ For ground state, $\mathrm{n}_{1}=1$ The Bohr radius of the $n^{\text {th }}$ state is $r=0.529 \frac{\mathrm{n}^{2}}{\mathrm{Z}} \AA$ $\text { So, } \mathrm{r} \propto \mathrm{n}^{2}$ $\therefore \frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{n}_{1}^{2}}{\mathrm{n}^{2}}$ For ground state $\left(\mathrm{n}_{1}\right)=1$ $\frac{5.3 \times 10^{-11} \mathrm{~m}}{21.2 \times 10^{-11} \mathrm{~m}}=\frac{1}{\mathrm{n}^{2}}$ $\mathrm{n}^{2}=4 \Rightarrow \mathrm{n}=2$
MHT-CET 2009
ATOMS
145280
If the unclear radius of ${ }^{27} \mathrm{AI}$ us $3.6 \mathrm{Fermi}$, the approximate nuclear radius of ${ }^{64} \mathrm{Cu}$ in Fermi is
145273
Assertion: The specific charge of positive rays is not constant. Reason: The mass of ions varies with speed.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason in not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
A The specific charge (e/m) of the positive rays is not constant because these rays may consist of ions of different elements and the mass of these ions varies with speed. Hence, option (a) is correct.
AIIMS-1999
ATOMS
145281
The ratio of volume occupied by an atom to the volume of the nucleus is
1 $10^{5}: 1$
2 $10^{20}: 1$
3 $10^{15}: 1$
4 $1: 10^{15}$
Explanation:
C We know that radius of atom $\left(\mathrm{r}_{\mathrm{a}}\right)=10^{-10} \mathrm{~m}$ and radius of nucleus $\left(\mathrm{r}_{\mathrm{n}}\right)=10^{-15} \mathrm{~m}$ Now, Ratio of the volume, $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{\frac{4}{3} \pi\left(10^{-10}\right)^{3}}{\frac{4}{3} \pi\left(10^{-15}\right)^{3}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{-30}}{10^{-45}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{15}}{1}$ $\mathrm{V}_{\mathrm{a}}: \mathrm{V}_{\mathrm{n}}=10^{15}: 1$
145279
The radius of hydrogen atom in its ground state is $5.3 \times 10^{-11} \mathrm{~m}$. After collision with an electron it is found to have a radius of $21.2 \times$ $10^{-11} \mathrm{~m}$. What is the principal quantum number $n$ of the final state of atom ?
1 $\mathrm{n}=4$
2 $n=2$
3 $\mathrm{n}=16$
4 $\mathrm{n}=3$
Explanation:
B Given, Radius of ground state $\left(\mathrm{r}_{1}\right)=5.3 \times 10^{-11} \mathrm{~m}$ Radius of $\mathrm{n}^{\text {th }}$ state $\left(\mathrm{r}_{2}\right)=21.2 \times 10^{-11} \mathrm{~m}$ For ground state, $\mathrm{n}_{1}=1$ The Bohr radius of the $n^{\text {th }}$ state is $r=0.529 \frac{\mathrm{n}^{2}}{\mathrm{Z}} \AA$ $\text { So, } \mathrm{r} \propto \mathrm{n}^{2}$ $\therefore \frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{n}_{1}^{2}}{\mathrm{n}^{2}}$ For ground state $\left(\mathrm{n}_{1}\right)=1$ $\frac{5.3 \times 10^{-11} \mathrm{~m}}{21.2 \times 10^{-11} \mathrm{~m}}=\frac{1}{\mathrm{n}^{2}}$ $\mathrm{n}^{2}=4 \Rightarrow \mathrm{n}=2$
MHT-CET 2009
ATOMS
145280
If the unclear radius of ${ }^{27} \mathrm{AI}$ us $3.6 \mathrm{Fermi}$, the approximate nuclear radius of ${ }^{64} \mathrm{Cu}$ in Fermi is
145273
Assertion: The specific charge of positive rays is not constant. Reason: The mass of ions varies with speed.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason in not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
A The specific charge (e/m) of the positive rays is not constant because these rays may consist of ions of different elements and the mass of these ions varies with speed. Hence, option (a) is correct.
AIIMS-1999
ATOMS
145281
The ratio of volume occupied by an atom to the volume of the nucleus is
1 $10^{5}: 1$
2 $10^{20}: 1$
3 $10^{15}: 1$
4 $1: 10^{15}$
Explanation:
C We know that radius of atom $\left(\mathrm{r}_{\mathrm{a}}\right)=10^{-10} \mathrm{~m}$ and radius of nucleus $\left(\mathrm{r}_{\mathrm{n}}\right)=10^{-15} \mathrm{~m}$ Now, Ratio of the volume, $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{\frac{4}{3} \pi\left(10^{-10}\right)^{3}}{\frac{4}{3} \pi\left(10^{-15}\right)^{3}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{-30}}{10^{-45}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{15}}{1}$ $\mathrm{V}_{\mathrm{a}}: \mathrm{V}_{\mathrm{n}}=10^{15}: 1$
145279
The radius of hydrogen atom in its ground state is $5.3 \times 10^{-11} \mathrm{~m}$. After collision with an electron it is found to have a radius of $21.2 \times$ $10^{-11} \mathrm{~m}$. What is the principal quantum number $n$ of the final state of atom ?
1 $\mathrm{n}=4$
2 $n=2$
3 $\mathrm{n}=16$
4 $\mathrm{n}=3$
Explanation:
B Given, Radius of ground state $\left(\mathrm{r}_{1}\right)=5.3 \times 10^{-11} \mathrm{~m}$ Radius of $\mathrm{n}^{\text {th }}$ state $\left(\mathrm{r}_{2}\right)=21.2 \times 10^{-11} \mathrm{~m}$ For ground state, $\mathrm{n}_{1}=1$ The Bohr radius of the $n^{\text {th }}$ state is $r=0.529 \frac{\mathrm{n}^{2}}{\mathrm{Z}} \AA$ $\text { So, } \mathrm{r} \propto \mathrm{n}^{2}$ $\therefore \frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{n}_{1}^{2}}{\mathrm{n}^{2}}$ For ground state $\left(\mathrm{n}_{1}\right)=1$ $\frac{5.3 \times 10^{-11} \mathrm{~m}}{21.2 \times 10^{-11} \mathrm{~m}}=\frac{1}{\mathrm{n}^{2}}$ $\mathrm{n}^{2}=4 \Rightarrow \mathrm{n}=2$
MHT-CET 2009
ATOMS
145280
If the unclear radius of ${ }^{27} \mathrm{AI}$ us $3.6 \mathrm{Fermi}$, the approximate nuclear radius of ${ }^{64} \mathrm{Cu}$ in Fermi is
145273
Assertion: The specific charge of positive rays is not constant. Reason: The mass of ions varies with speed.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason in not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
A The specific charge (e/m) of the positive rays is not constant because these rays may consist of ions of different elements and the mass of these ions varies with speed. Hence, option (a) is correct.
AIIMS-1999
ATOMS
145281
The ratio of volume occupied by an atom to the volume of the nucleus is
1 $10^{5}: 1$
2 $10^{20}: 1$
3 $10^{15}: 1$
4 $1: 10^{15}$
Explanation:
C We know that radius of atom $\left(\mathrm{r}_{\mathrm{a}}\right)=10^{-10} \mathrm{~m}$ and radius of nucleus $\left(\mathrm{r}_{\mathrm{n}}\right)=10^{-15} \mathrm{~m}$ Now, Ratio of the volume, $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{\frac{4}{3} \pi\left(10^{-10}\right)^{3}}{\frac{4}{3} \pi\left(10^{-15}\right)^{3}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{-30}}{10^{-45}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{15}}{1}$ $\mathrm{V}_{\mathrm{a}}: \mathrm{V}_{\mathrm{n}}=10^{15}: 1$
145279
The radius of hydrogen atom in its ground state is $5.3 \times 10^{-11} \mathrm{~m}$. After collision with an electron it is found to have a radius of $21.2 \times$ $10^{-11} \mathrm{~m}$. What is the principal quantum number $n$ of the final state of atom ?
1 $\mathrm{n}=4$
2 $n=2$
3 $\mathrm{n}=16$
4 $\mathrm{n}=3$
Explanation:
B Given, Radius of ground state $\left(\mathrm{r}_{1}\right)=5.3 \times 10^{-11} \mathrm{~m}$ Radius of $\mathrm{n}^{\text {th }}$ state $\left(\mathrm{r}_{2}\right)=21.2 \times 10^{-11} \mathrm{~m}$ For ground state, $\mathrm{n}_{1}=1$ The Bohr radius of the $n^{\text {th }}$ state is $r=0.529 \frac{\mathrm{n}^{2}}{\mathrm{Z}} \AA$ $\text { So, } \mathrm{r} \propto \mathrm{n}^{2}$ $\therefore \frac{\mathrm{r}_{1}}{\mathrm{r}_{2}}=\frac{\mathrm{n}_{1}^{2}}{\mathrm{n}^{2}}$ For ground state $\left(\mathrm{n}_{1}\right)=1$ $\frac{5.3 \times 10^{-11} \mathrm{~m}}{21.2 \times 10^{-11} \mathrm{~m}}=\frac{1}{\mathrm{n}^{2}}$ $\mathrm{n}^{2}=4 \Rightarrow \mathrm{n}=2$
MHT-CET 2009
ATOMS
145280
If the unclear radius of ${ }^{27} \mathrm{AI}$ us $3.6 \mathrm{Fermi}$, the approximate nuclear radius of ${ }^{64} \mathrm{Cu}$ in Fermi is
145273
Assertion: The specific charge of positive rays is not constant. Reason: The mass of ions varies with speed.
1 If both Assertion and Reason are correct and the Reason is a correct explanation of the Assertion.
2 If both Assertion and Reason are correct but Reason in not a correct explanation of the Assertion.
3 If the Assertion is correct but Reason is incorrect.
4 If both the Assertion and Reason are incorrect.
5 If the Assertion is incorrect but the Reason is correct.
Explanation:
A The specific charge (e/m) of the positive rays is not constant because these rays may consist of ions of different elements and the mass of these ions varies with speed. Hence, option (a) is correct.
AIIMS-1999
ATOMS
145281
The ratio of volume occupied by an atom to the volume of the nucleus is
1 $10^{5}: 1$
2 $10^{20}: 1$
3 $10^{15}: 1$
4 $1: 10^{15}$
Explanation:
C We know that radius of atom $\left(\mathrm{r}_{\mathrm{a}}\right)=10^{-10} \mathrm{~m}$ and radius of nucleus $\left(\mathrm{r}_{\mathrm{n}}\right)=10^{-15} \mathrm{~m}$ Now, Ratio of the volume, $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{\frac{4}{3} \pi\left(10^{-10}\right)^{3}}{\frac{4}{3} \pi\left(10^{-15}\right)^{3}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{-30}}{10^{-45}}$ $\frac{\mathrm{V}_{\mathrm{a}}}{\mathrm{V}_{\mathrm{n}}}=\frac{10^{15}}{1}$ $\mathrm{V}_{\mathrm{a}}: \mathrm{V}_{\mathrm{n}}=10^{15}: 1$
