Atoms Test

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Atoms Test - 79

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Weekly Quiz Competition

Question 1
1 / -0

The ratio of the largest to shortest wavelength in Lyman series of hydrogen spectra is

A
$$ \dfrac { 25 }{ 9 } $$

B
$$\dfrac { 17 }{ 6 }$$

C
$$ \dfrac { 9 }{ 5}$$

D
$$\dfrac { 4 }{ 3 }$$

Solution

For Lyman series $$\dfrac {1}{\lambda_{max}}=R \left[ \dfrac {1}{1^2}-\dfrac {1}{2^2}\right]=\dfrac 34\ R$$ and
$$\dfrac {1}{\lambda_{min}}=R\left[ \dfrac {1}{1^2}-\dfrac{1}{\infty^2}\right]=\dfrac R1$$
$$ \Rightarrow \dfrac{\lambda_{max}}{\lambda_{min}}=\dfrac {4}{3}$$
Question 2
1 / -0

The wavelength of the least energetic photon in the Balmer spectrum of hydrogen atom is:

A
$$365nm$$

B
$$665nm$$

C
$$912nm$$

D
$$725nm$$

Solution
Question 3
1 / -0

The hydrogen atom in ground state is excited by a monochromatic radiation of $$ \lambda=975 A^{\circ} $$ . Number of spectral lines in the resulting spectrum emitted will be

A
3

B
2

C
6

D
10

Solution
Question 4
1 / -0

An excited electron of H-atoms emits a photon of wavelength λ and returns in the ground state, the principal quantum number of excited state is given by:

A
$$\sqrt{ [(λR-1)/(λR)]}$$

B
$$\sqrt{ [(λR)/(λR-1)]}$$

C
$$\sqrt{ [λR(λR-1)]}$$

D
$$λR(R-1)$$
Question 5
1 / -0

The radius of which of the following orbit is same as that of the first Bohr's orbit of hydrogen atom

A
$${ He }^{ + }(n=2)$$

B
$${ Li }^{ 2+ }(n=2)$$

C
$${ Li }^{ 2+ }(n=3)$$

D
$$\ { Be }^{ 3+ }(n=2)$$
Question 6
1 / -0

The relation between $${\lambda}_{1}$$: wavelength of series limit of Lyman series, $${\lambda}_{0}$$: the wavelength of the series limit of Balmer series and $${\lambda}_{3}$$: the wavelength of first line of Lyman series is:

A
$${\lambda}_{1}={\lambda}_{2}+{\lambda}_{3}$$

B
$${\lambda}_{3}={\lambda}_{1}+{\lambda}_{2}$$

C
$${\lambda}_{2}={\lambda}_{3}+{\lambda}_{1}$$

D
None of these

Solution
Question 7
1 / -0

In hydrogen atom electron is revolving around nucleus in circular orbit with frequency of $$6.57 \times {1^{15}}$$ revolutions. If its equivalent magnetic moment is $$9.24 \times {10^{ - 24}}A{m^2}$$ , the radius of orbit of electron is

A
0.27 A

B
0.53 A

C
1.27 A

D
1.34 A

Solution
Question 8
1 / -0

According to the Bohr theory of the hydrogen atom electrons starting in the $$4^{th}$$ energy level and eventually ending in the ground state could produce a total of how many lines in the hydrogen spectra ?

A
7

B
6

C
5

D
4
Question 9
1 / -0

Heat treatment of muscular pain involves radiation of wavelength of about 900 nm. Which spectral line H-atom is suitable for this purpose ?
Given: $${ R }_{ H }=1\times { 10 }^{ 5 }cm, h=6.610^{ -34 }Js, C=3\times 10^{ 4}m/{ s }^{ -1 }$$

A
Paschen $$5\rightarrow 3$$

B
Paschen $$\infty \rightarrow 3$$

C
Lyman, $$\infty \rightarrow 1$$

D
Balmer $$\infty \rightarrow 2$$

Solution
Question 10
1 / -0

The frequency of first line of Balmer series in hydrogen atom is $$v_0$$. The frequency of corresponding line emitted by singly ionised helium atom is -

A
$$2 v_0$$

B
$$4 v_0$$

C
$$v_0/2$$

D
$$v_0/4$$

Solution

$$v \propto Z^2 \Rightarrow \dfrac{v_{H_2}}{v_{He}}=\left( \dfrac 12 \right)^2=\dfrac 14 $$
$$\Rightarrow v_{He}=4v_{H_2}=4v_0$$