Atoms

1. A.
   $\frac{1}{n^2}$
2. B.
   $\frac{1}{n}$
3. C.
   n
4. D.
   $n^2$

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1. A.
   $\sqrt{n}$
2. B.
   n
3. C.
   $n^2$
4. D.
   $n^3$

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1. A.
   $\frac{\nu}{3}$
2. B.
   $\frac{\nu}{4}$
3. C.
   $\frac{\nu}{5}$
4. D.
   $\frac{\nu}{6}$

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1. A.
   2d
2. B.
   d
3. C.
   $\frac{d}{2}$
4. D.
   $\frac{d}{\sqrt{2}}$

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1. A.
   $-\frac{1}{2}$
2. B.
   $\frac{1}{2}$
3. C.
   2
4. D.
   $-2$

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1. A.
   $\frac{d}{2}$
2. B.
   2d
3. C.
   $\frac{d}{4}$
4. D.
   4d

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1. A.
   $1.05 \times 10^{-34}$ J s
2. B.
   $6.63 \times 10^{-34}$ J s
3. C.
   $3.31 \times 10^{-34}$ J s
4. D.
   $2.1 \times 10^{-34}$ J s

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1. A.
   n
2. B.
   $\mathrm{n^2}$
3. C.
   $\mathrm{n^3}$
4. D.
   $\mathrm{n^4}$

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1. A.
   $\dfrac{3h}{2\pi}$
2. B.
   $\dfrac{2h}{\pi}$
3. C.
   $\dfrac{h}{\pi}$
4. D.
   $\dfrac{h}{2\pi}$

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1. A.
   2
2. B.
   $\dfrac{1}{2}$
3. C.
   3
4. D.
   $\dfrac{1}{3}$

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1. A.
   infrared region
2. B.
   ultraviolet region
3. C.
   visible region
4. D.
   partly in ultraviolet region and partly in visible region

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1. A.
   $\frac{8}{7}\lambda$
2. B.
   $\frac{24}{7}\lambda$
3. C.
   $\frac{16}{7}\lambda$
4. D.
   $\frac{32}{7}\lambda$

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1. A.
   $n^2$
2. B.
   n
3. C.
   $\dfrac{1}{n}$
4. D.
   $\dfrac{1}{n^2}$

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Both Assertion (A) and Reason (R) are false.

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1. A.
   $3{\cdot}4$ eV
2. B.
   less than $3{\cdot}4$ eV
3. C.
   $13{\cdot}6$ eV
4. D.
   between $13{\cdot}6$ eV and $3{\cdot}4$ eV

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1. A.
   n = 4 to n = 3
2. B.
   n = 3 to n = 2
3. C.
   n = 2 to n = 1
4. D.
   n = 3 to n = 1

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1. A.
   2
2. B.
   3
3. C.
   4
4. D.
   5

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1. A.
   If both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. B.
   If both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
3. C.
   If Assertion (A) is true but Reason (R) is false.
4. D.
   If both Assertion (A) and Reason (R) are false.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Both Assertion (A) and Reason (R) are false.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Both Assertion (A) and Reason (R) are false.

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1. A.
   Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
2. B.
   Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
3. C.
   Assertion (A) is true, but Reason (R) is false.
4. D.
   Assertion (A) is false and Reason (R) is also false.

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1. A.
   $\dfrac{Ke^2}{mr}$
2. B.
   $\dfrac{Ke^2}{mr^2}$
3. C.
   $\sqrt{\dfrac{Ke^2}{mr}}$
4. D.
   $\sqrt{\dfrac{Ke^2}{mr^2}}$

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1. A.
   $\dfrac{Ke^2}{r}$
2. B.
   $-\dfrac{Ke^2}{2r}$
3. C.
   $\dfrac{Ke^2}{2r}$
4. D.
   $\dfrac{3}{2}\,\dfrac{Ke^2}{r}$

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1. A.
   $2{\cdot}48,\ -2{\cdot}48$
2. B.
   $-1{\cdot}24,\ 1{\cdot}24$
3. C.
   $-2{\cdot}48,\ 2{\cdot}48$
4. D.
   $1{\cdot}24,\ -1{\cdot}24$

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1. A.
   $n$
2. B.
   $\dfrac{1}{n}$
3. C.
   $\dfrac{1}{n^2}$
4. D.
   $\dfrac{1}{n^3}$

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1. A.
   $0{\cdot}53$ Å
2. B.
   $1{\cdot}06$ Å
3. C.
   $1{\cdot}59$ Å
4. D.
   $2{\cdot}12$ Å

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1. A.
   $r_n \propto n$
2. B.
   $r_n \propto \dfrac{1}{n}$
3. C.
   $r_n \propto n^2$
4. D.
   $r_n \propto \dfrac{1}{n^2}$

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1. A.
   $\lambda_1^2 + \lambda_2^2 = \lambda_3^2$
2. B.
   $\dfrac{1}{\lambda_1} + \dfrac{1}{\lambda_2} = \dfrac{1}{\lambda_3}$
3. C.
   $\lambda_1 + \lambda_2 + \lambda_3 = 0$
4. D.
   $\lambda_1 + \lambda_2 = \lambda_3$

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1. A.
   $-13.6$ eV, $27.2$ eV
2. B.
   $-6.8$ eV, $13.6$ eV
3. C.
   $3.4$ eV, $-6.8$ eV
4. D.
   $6.8$ eV, $-3.4$ eV

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1. A.
   $\dfrac{1}{2}$
2. B.
   2
3. C.
   $\dfrac{1}{4}$
4. D.
   4

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1. A.
   $\mathrm{n}_f = 2$ and $\mathrm{n}_i = 3$
2. B.
   $\mathrm{n}_f = 3$ and $\mathrm{n}_i = 4$
3. C.
   $\mathrm{n}_f = 2$ and $\mathrm{n}_i = 4$
4. D.
   $\mathrm{n}_f = 2$ and $\mathrm{n}_i = \infty$

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1. A.
   $\dfrac{1}{\sqrt{K}}$
2. B.
   $\sqrt{K}$
3. C.
   $\dfrac{1}{K}$
4. D.
   $K$

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1. A.
   increases by $87{\cdot}5\%$
2. B.
   decreases by $87{\cdot}5\%$
3. C.
   increases by $43{\cdot}75\%$
4. D.
   decreases by $43{\cdot}75\%$

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1. A.
   equally spaced and equally intense.
2. B.
   further apart and stronger in intensity.
3. C.
   closer together and stronger in intensity.
4. D.
   closer together and weaker in intensity.

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1. A.
   If both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
2. B.
   If both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).
3. C.
   If Assertion (A) is true but Reason (R) is false.
4. D.
   If both Assertion (A) and Reason (R) are false.

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1. A.
   n = 3 to n = 1
2. B.
   n = 3 to n = 2
3. C.
   n = 4 to n = 1
4. D.
   n = 4 to n = 2

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1. A.
   I
2. B.
   II
3. C.
   III
4. D.
   IV

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1. A.
   $\dfrac{1}{n^2}$
2. B.
   $\dfrac{1}{n}$
3. C.
   $n^2$
4. D.
   $n$

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1. A.
   $\dfrac{8}{7}\lambda$
2. B.
   $\dfrac{16}{7}\lambda$
3. C.
   $\dfrac{24}{7}\lambda$
4. D.
   $\dfrac{32}{7}\lambda$

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1. A.
   975 nm
2. B.
   740 nm
3. C.
   523 nm
4. D.
   95 nm

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1. A.
   $\dfrac{11}{9}$
2. B.
   $\dfrac{9}{5}$
3. C.
   $\dfrac{11}{7}$
4. D.
   $\dfrac{16}{7}$

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1. A.
   $-3{\cdot}4$ eV
2. B.
   $-3{\cdot}02$ eV
3. C.
   $-1{\cdot}51$ eV
4. D.
   $-6{\cdot}8$ eV

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1. A.
   $n^2$
2. B.
   $\dfrac{1}{n^2}$
3. C.
   $n$
4. D.
   $\dfrac{1}{n}$

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