Atoms Test

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Atoms Test - 58

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Weekly Quiz Competition

Question 1
1 / -0

The anode voltage of a photocell is kept fixed. The wavelength (i) of light falling on the cathode is gradually changed. The plate current (I) of the photocell varies as

A

B

C

D

Solution

As $$\lambda$$ is increased, there will be a value of $$\lambda$$ above which photo electrons will cease to come out. So, photo current will be zero.
Question 2
1 / -0

The shortest wavelength in the Lyman series of hydrogen spectrum is 912 A corresponding to a photon energy of 13.6 eV. The shortest wavelength in the Balmer series is:

A
$$3648 A^o$$

B
$$228 A^o$$

C
$$6566 A^o$$

D
$$8208 A^o$$

Solution
Question 3
1 / -0

Time taken for an electron to complete one revolution in the Bohr orbit of hydrogen atom is:

A
$$\dfrac { 4\pi ^{ 2 }mr^{ 2 } }{ nh } $$

B
$$\dfrac { nh }{ 4{ \pi }^{ 2 }mr } $$

C
$$\dfrac { nh }{ 4{ \pi }^{ 2 }mr^{ 2 } } $$

D
$$\dfrac { h }{ 2\pi mr } $$

Solution

By Bohr postulate, $$ mvr = n \dfrac{h}{2 \pi} $$ or $$ v = \dfrac{nh}{2 \pi m r } $$

No. of revolutions per sec

$$ = \dfrac{{\text{Velocity}}}{{\text{Circumference of the orbit}}} $$

$$ = \dfrac{v}{2 \pi r } = \dfrac{nh}{2 \pi m r} \times \dfrac{1}{2 \pi r} = \dfrac{nh}{4 \pi^2 mr^2} $$

Time taken for one revolution $$ = \dfrac{4 \pi^2 mr^2}{nh} $$
Question 4
1 / -0

From lyman series of Pfund series, frequency__________

A
increase

B
decrease

C
increase or decrease

D
no change

Solution

In physics and chemistry the lyman series is a hydrogen spectral series transitions and resulting ultraviolet emission lines of the hydrogen atom as electron goes from $$n \geqslant 2\,to\,n = 1.$$
So$$,$$ lyman series of pfund series$$,$$ frequency is decrease$$.$$
hence,
option $$(B)$$ is correct answer.
Question 5
1 / -0

The energy of electron in the excited state of hydrogen atom is $$-0.85 eV$$. If 'h' is Plank's constant, the angular momentum of electron in the excited state is :

A
$$\dfrac{4h}{2 \pi}$$

B
$$h$$

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

D
$$\dfrac{h}{\pi}$$

Solution

Energy of the $$nth$$ state of H-atom $$E_n = \dfrac{-13.6}{n^2} \ eV$$
So, $$-0.85 = -\dfrac{13.6}{n^2}$$
Or $$n^2 = \dfrac{13.6}{0.85} = 16$$
$$\implies \ n = 4$$
Angular momentum $$L = \dfrac{nh}{2\pi} = \dfrac{4h}{2\pi}$$
Question 6
1 / -0

Two monochromatic light sources, $$A$$ and $$B$$, emit the same number of photons per second. The wavelength of $$A$$ is $${\lambda}_{A}=400nm$$ and that $$B$$ is $${\lambda}_{B}=600nm$$. The power radiated by source $$B$$ is

A
equal to that of source $$A$$

B
less than that of source $$A$$

C
greater than that of source $$A$$

D
cannot be compared to that from source $$A$$ using the available data.
Question 7
1 / -0

In hydrogen atom, an electron makes transition from $$n=3$$ to $$n=2$$ state in time interval of $$1.2\times{10}^{-8}s$$. Calculate the average torque (in Nm) acting on the electron during this transition.

A
$$1.055\times{10}^{-26}$$

B
$$4.40\times{10}^{-27}$$

C
$$1.7\times{10}^{-26}$$

D
$$8.79\times{10}^{-27}$$

Solution

Given,
$$t=1.2\times 10^{-8}sec$$
By Bohr's model,
Angular momentum,$$L=\dfrac{nh}{2\pi}$$
$$n=3$$, $$L_3=\dfrac{3h}{2\pi}$$
$$n=2$$, $$L_2=\dfrac{2h}{2\pi}$$
Torque is the rate of change of angular momentum
$$\tau=\dfrac{L_2-L_3}{t}$$
$$\tau=\dfrac{(2h/2\pi)-(3h/2\pi)}{t}$$
$$|\tau|=\dfrac{h}{2\pi t}$$
$$|\tau|=\dfrac{6.65\times 10^{-34}}{2\times 3.14\times 1.2\times 10^{-8}}$$
$$|\tau|=1.055\times 10^{-26}Nm$$
The correct option is A.
Question 8
1 / -0

In the following transitions, which one has higher frequency?

A
$$3 - 2$$

B
$$4 - 3$$

C
$$4 - 2$$

D
$$3 - 1$$

Solution

$$3-1$$ transition has higher energy so it has higher frequency
$$\left( v=\dfrac{E}{h}\right)$$
Question 9
1 / -0

In which of the following system will the radius of the $$2^{nd}$$ orbit be minimum?

A
$$H$$

B
$$Mg^{+2}$$

C
$$He^+$$

D
$$B$$

Solution
Question 10
1 / -0

Suppose an electron is attracted towards the origin by a force $$\dfrac { k }{ r } $$ where 'k' is a constant and 'y' is the distance of the electron form the origin. By applying Bohr model to this system, the radius of the nth orbital of the electron is found to be 'r$$_{ n }$$' and the kinetic energy of the electron to be 'T$$_{ n }$$'. Then which of the following is true ?

A
$${ T }_{ n }$$ independent of n,

B
$${ T }_{ n }\propto \dfrac { 1 }{ n } ,{ r }_{ n }\propto n$$

C
$${ T }_{ n }\mu \dfrac { 1 }{ n } { n }_{ 1 },{ r }_{ n }\propto n^{ 2 }$$

D
$${ T }_{ n }\mu \dfrac { 1 }{ n^{ 2 } } ,{ r }_{ n }\propto n^{ 2 }$$