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NEET NEET Questions — Free MCQ Practice

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The first line of Balmer series has wavelength 6563 Å. What will be the wavelength of the first member of Lyman series

A.

1215.4 Å

B.

2500 Å

C.

7500 Å

D.

600 Å

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Explanation

(a) $\frac{1}{λ_{Balmer}} = R [\frac{1}{1^{2}} - \frac{1}{2^{2}}] = \frac{3 R}{4} ∴ λ_{Lyman} = λ_{Balmer} \times \frac{5}{27} = 1215.4 \overset{0}{A}$

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In Bohr's model, the atomic radius of the first orbit is $r_{0}$ , then the radius of the third orbit is

A.

$\frac{r_{0}}{9}$

B.

$r_{0}$

C.

$9 r_{0}$

D.

$3 r_{0}$

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Explanation

(c) $r_{n} \propto n^{2}$

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The wavelength of the energy emitted when electron come from fourth orbit to second orbit in hydrogen is 20.397 cm. The wavelength of energy for the same transition in ${He}^{+}$ is

A.

5.099 ${cm}^{- 1}$

B.

20.497 ${cm}^{- 1}$

C.

40.994 ${cm}^{- 1}$

D.

81.988 ${cm}^{- 1}$

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Explanation

(a) $E (= \frac{hc}{λ}) \propto \frac{Z^{2}}{n^{2}} \Rightarrow λ \propto \frac{1}{Z^{2}}$

Hence $λ_{{He}^{+}} = \frac{20.397}{4} = 5.099 cm$

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Minimum excitation potential of Bohr's first orbit in hydrogen atom is

A.

13.6 V

B.

3.4 V

C.

10.2 V

D.

3.6 V

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Explanation

(c) Excitation potential = $\frac{Excitation energy}{e}$
Minimum excitation energy corresponds to excitation from n =1 to n = 2
$∴$ Minimum excitation energy in hydrogen atom = -3.4-(-13.6) = +10.2 eV

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Which of the following statements are true regarding Bohr's model of hydrogen atom

(I) Orbiting speed of electron decreases as it shifts to
discrete orbits away from the nucleus

(II) Radii of allowed orbits of electron are proportional to the cube of principal quantum number

(III) Frequency with which electrons orbits around the nucleus in discrete orbits is inversely proportional to the principal quantum number

(IV) Binding force with which the electron is bound to the nucleus increases as it shifts to outer orbits
Select correct answer using the codes given below
Codes :

A.

I and III

B.

II and IV

C.

I, II and III

D.

II, III and IV

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Explanation

(a) Orbital speed varies inversely as the radius of the orbit. Energy increases with the increase in quantum number.

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For electron moving in $n^{th}$ orbit of H-atom the angular velocity is proportional to

A.

n

B.

1/n

C.

$n^{3}$

D.

1/ $n^{3}$

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Explanation

(d) Radius of nth orbit, $r_{n} α \frac{1}{n^{2}}$

Velocity of electron, $v_{n} α \frac{1}{n}$

$∴ A n g u l a r v e l o c i t y, ω_{n} = \frac{v_{n}}{r_{n}} \Rightarrow ω_{n} α \frac{1}{n^{3}}$

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The energy of electron in first excited state of H-atom is -3.4 eV its kinetic energy is

A.

– 3.4 eV

B.

+ 3.4 eV

C.

– 6.8 eV

D.

6.8 eV

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Explanation

(b) Kinetic energy = |Total energy|

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Which of the following phenomena suggests the presence of electron energy levels in atoms?

A.

Radio active decay

B.

Isotopes

C.

Spectral lines

D.

$α$ -particles scattering

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Explanation

(c) Spectral lines result from emission or absorption of energy due to difference in energy levels of electrons.

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Which of the following spectral series in hydrogen atom give spectral line of 4860 Å

A.

Lyman

B.

Balmer

C.

Paschen

D.

Brackett

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Explanation

(b) For Balmer series :

$λ_{m i n} = 3648 \overset{o}{A} λ_{m a x} = 6563 \overset{o}{A}$

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When an electron in hydrogen atom is excited, from its 4th to 5th stationary orbit, the change in angular momentum of electron is (Planck’s constant: h = $6.6 \times 10^{- 34} J - s$ 6.6)

A.

$4.16 \times 10^{- 34} J - s$

B.

$3.32 \times 10^{- 34} J - s$

C.

$1.05 \times 10^{- 34} J - s$

D.

$2.08 \times 10^{- 34} J - s$

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Explanation

(c) Change in the angular momentum

$∆ L = L_{2} - L_{1} = \frac{n_{2} h}{2 π} - \frac{n_{1} h}{2 π} \Rightarrow ∆ L = \frac{h}{2 π} (n_{2} - n_{1}) = \frac{6.6 \times 10^{- 34}}{2 \times 3.14} (5 - 4) = 1.05 \times 10^{- 34} J - s$

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