Atoms Test

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Atoms Test - 54

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Weekly Quiz Competition

Question 1
1 / -0

Dynamic mass of the photon in usual notations is given by -

A
$$\dfrac { h v } { c }$$

B
$$\dfrac { h \lambda } { c }$$

C
$$\dfrac { h } { c \lambda }$$

D
$$\dfrac { h } { c v }$$

Solution

$$\begin{array}{l}\text { From Einstien's theory of relativity, }\\\text { We can say that } \\\qquad E=m c^{2} \\\text { E is energy of ; } E=\dfrac{h c}{\lambda} \\\qquad \begin{array}{l}m=\dfrac{h}{c\lambda}\end{array}\end{array}$$
Question 2
1 / -0

Which of the following postulates of the Bohr model led to the quantization of energy of the hydrogen atom?

A
The electron goes around the nucleus in circular orbits.

B
The angular momentum of the electron can only be an integral multiple of $$h/2\pi$$.

C
The magnitude of the linear momentum of the electron is quantized

D
Quantization of energy is itself a postulate of the Bohr model.

Solution

$$\begin{array}{l}\text { Quantization of of energy of the } \\\text { hydrogen atom is lead by } \\\text { angular momentum of the electron can } \\\text { only be an integral multiple of } \\h / 2 \pi.\end{array}$$
Question 3
1 / -0

a diatomic has a moment of inertia.By Bohr's quantization condition its rotational energy in the $$n^{th}$$ level ( n= 0 is not allowed ) is :

A
$$\frac{1}{n^{2}}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

B
$$\frac{1}{n}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

C
$$n\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

D
$$n^{2}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

Solution

$$\begin{array}{l}\qquad V=R \omega \text { , } \omega \text { is Angular velocity. } \\\text { Moment of inertia, } I=m R^{2} \\\text { Bohr's Angular momentum, } \\\qquad \begin{array}{l}m V R=\frac{n h}{2\pi} \\m \omega R^{2}=\frac{n h}{2 \pi}\end{array}\end{array}$$

$$\begin{array}{l}\qquad w=\frac{n h}{2 \pi m R^{2}} \\\text { Rotational energy } \\\qquad \begin{aligned}R \cdot E &=\frac{1}{2} I\omega^{2} \\&=\frac{1}{2} m R^{2} \times \frac{n^{2} h^{2}}{4\pi^{2}\left(m R^{2}\right)^{2}} \\R \cdot E&=n^{2}\left(\frac{n^{2}}{8 \pi^{2} m Q^{2}}\right) \\\therefore & R \cdot E=n^{2}\left(\frac{h^{2}}{8 \pi^{2} I}\right)\end{aligned}\end{array}$$
Question 4
1 / -0

The orbital angular moments of an electron is $$\sqrt 3 \cfrac h {\pi}$$.Which of the following may be the permissible value of angular momentum of this electron revolving in an unknown orbit.

A
$$\cfrac h {\pi}$$

B
$$\cfrac h {2\pi}$$

C
$$\cfrac {3h} {2\pi}$$

D
$$\cfrac {2h} {\pi}$$

Solution

$$\begin{array}{l}\text { Given: orbital angular momentum, }\\\qquad\begin{aligned}\sqrt{l(l+1)} \frac{h}{2 \pi}=\sqrt{3} \frac{h}{\pi} \\\frac{l(l+1)}{4} &=3 \\\ell (l+1) &=3(3+1) \\\therefore & l=3\end{aligned}\end{array}$$

$$\begin{array}{l}\text { since, } l=3 \\\text { permissible values of } n \text { are } 4,5,6, \ldots . \\\text { Angular momentum can be }\frac{2 h}{\pi} \text { , } \frac{5 h}{2 \pi}, \frac{3 h}{\pi} \text { , } \ldots \\\therefore \quad \frac{2 h}{\pi}\end{array}$$
Question 5
1 / -0

In a hydrogen atom the force acting on the electron is proportional to :

A
$$n^{4}$$

B
$$n^{-4}$$

C
$$r^{2}$$

D
$$n^{-2}$$

Solution

A hydrogen atom the force acting on the election is proportional to $$r^2$$.
Hence ,option $$C$$ is correct.
Question 6
1 / -0

$$2N$$ molecules of an ideal gas '$$X$$' each of mass '$$m$$' and $$4N$$ molecules of another ideal gas $$Y,$$ each of mass $$3m$$ are maintained at the same absolute temperature in the same vessel. The rms velocity are $$V1$$ and $$V2$$ respectively then (along x-coordinate axis)$$\dfrac{v_x}{v_y}$$

A
$$\sqrt { 3 } : 1$$

B
$$1 : \sqrt { 3 }$$

C
$$3 : 1$$

D
$$1 : 3$$

Solution

$$\begin{array}{l}\text { R.M.S velocity, Vrms } \alpha \sqrt{\frac{T}{m}} \\\qquad \begin{array}{l}T_{1}=T_{2} \\m_{1}=m \\m_{2}=3 m\end{array} \\\therefore \quad \frac{V_{1}}{V_{2}}=\sqrt{3} \\\text { Required ratio is } \sqrt{3}: 1\end{array}$$
Question 7
1 / -0

Alpha particles are projected towards fixed at a nucleus. Which of the paths shown in figure, is not possible

A
1

B
2

C
3

D
4

Solution

Trajectory 3 is not possible because alpha particle will repel alpha particle so trajectory 3 is showing attraction so it is not possible.
Question 8
1 / -0

An electron tube was sealed off during manufacture at a pressure of $$1.2 \times 10^{-7}$$ mm of mercury at $$27^oC$$. Its volume is $$100 cm^3$$. The number of molecules that remain in the tube is

A
$$2 \times 10^{16}$$

B
$$3 \times 10^{15}$$

C
$$3.86 \times 10^{11}$$

D
$$5 \times 10^{11}$$

Solution

$$P=nkT\\ n=\cfrac { P }{ kT } =\cfrac { hdg }{ kT } $$
Number of molecules in the electron tube is$$=n\times V=\cfrac { hdgV }{ kT } $$
$$\Longrightarrow n=\cfrac { hdg }{ kT } =\cfrac { 1.2\times { 10 }^{ -10 }\times 13600\times 9.8\times 100\times { 10 }^{ -6 } }{ 1.38\times { 10 }^{ -23 }\times 300 } =3.86\times { 10 }^{ 11 }$$
Question 9
1 / -0

Orbital acceleration of electron in first orbit of hydrogen atom is:

A
$$\cfrac{h}{2\pi^2m^2r^3}$$

B
$$\cfrac{h^2}{2\pi^2m^2r^3}$$

C
$$\cfrac{h^2}{4\pi^2m^2r^3}$$

D
$$\cfrac{h^2}{4\pi^2m^2r^2}$$

Solution

Orbital Angular momentum
$$mvr=\dfrac{nh}{2\pi }$$ n=1

$$mvr=\dfrac{h}{2\pi }$$

$$v=\dfrac{h}{2\pi mr}$$

$$v^{2}=\left ( \dfrac{h}{2\pi mr} \right )^{2}$$

$$a=\dfrac{V^{2}}{r}=\dfrac{h^{2}}{4\pi ^{2}m^{2}r^{3}}$$
Question 10
1 / -0

Equivalent electric current created by electron of a H-atom in its ground using Bohr's model is nearly

A
$$2.14\times {10}^{-35}A$$

B
$$4.48\times {10}^{-30}A$$

C
$$24\times {10}^{-30}A$$

D
$$70\times {10}^{-35}A$$

Solution

$$\begin{array}{l}\text { Let, radius of } 1^{\text {St }} \text { orbit Atom be "a_o" } \\\text { velocity of } e^{-} \text { in } 1^{\text {st }} \text { orbit is } v \\\text { Time period, }\left[T=\dfrac{2 \pi \cdot a_{0}}{v}]--(1)\right] \end{array}$$

$$\begin{array}{l}\text { Electric current, } i=\dfrac{q}{T} \\\text { From } \\\qquad i=\dfrac{q v}{2 \pi a_{0}}\end{array}$$

$$\begin{array}{l}\text { By keeping approximate experimental } \\\text { values in above expression, we get } \\\qquad i=4.489 \times 10^{-30} A\end{array}$$

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Re-Attempt Weekly Quiz Competition

Atoms Test - 54

Result

Atoms Test - 54

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SHARING IS CARING

Question 1

$$\dfrac { h v } { c }$$

$$\dfrac { h \lambda } { c }$$

$$\dfrac { h } { c \lambda }$$

$$\dfrac { h } { c v }$$

Solution

Question 2

The electron goes around the nucleus in circular orbits.

The angular momentum of the electron can only be an integral multiple of $$h/2\pi$$.

The magnitude of the linear momentum of the electron is quantized

Quantization of energy is itself a postulate of the Bohr model.

Solution

Question 3

$$\frac{1}{n^{2}}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

$$\frac{1}{n}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

$$n\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

$$n^{2}\left ( \frac{h^{2}}{8\pi ^{2}I} \right )$$

Solution

Question 4

$$\cfrac h {\pi}$$

$$\cfrac h {2\pi}$$

$$\cfrac {3h} {2\pi}$$

$$\cfrac {2h} {\pi}$$

Solution

Question 5

$$n^{4}$$

$$n^{-4}$$

$$r^{2}$$

$$n^{-2}$$

Solution

Question 6

$$\sqrt { 3 } : 1$$

$$1 : \sqrt { 3 }$$

$$3 : 1$$

$$1 : 3$$

Solution

Question 7

1

2

3

4

Solution

Question 8

$$2 \times 10^{16}$$

$$3 \times 10^{15}$$

$$3.86 \times 10^{11}$$

$$5 \times 10^{11}$$

Solution

Question 9

$$\cfrac{h}{2\pi^2m^2r^3}$$

$$\cfrac{h^2}{2\pi^2m^2r^3}$$

$$\cfrac{h^2}{4\pi^2m^2r^3}$$

$$\cfrac{h^2}{4\pi^2m^2r^2}$$

Solution

Question 10

$$2.14\times {10}^{-35}A$$

$$4.48\times {10}^{-30}A$$

$$24\times {10}^{-30}A$$

$$70\times {10}^{-35}A$$

Solution

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