Modern Physics Mock Test-3

If the wavelength of the first line of the Balmer series of hydrogen atom is 6561Å, the wavelength of the second line of the series should be

[A] 13122Å
[B] 3280Å
[C] 4860Å
[D] 2187Å

An electron makes a transition from orbit n =4 to the orbit n = 2 of a hydrogen atom. The wave number of the emitted radiations (R = Rydberg’s constant) will be

[A] \( \frac{16}{3R}\)

[B] \( \frac{2R}{16}\)

[C] \( \frac{3R}{16}\)

[D] \( \frac{4R}{16}\)

The wavelength of radiation emitted is λ0 when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit [A] \( \frac{16}{25}\)λ0

[B] \( \frac{20}{27}\)λ0

[C] \( \frac{27}{20}\)λ0

[D] \( \frac{25}{16}\)λ0

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 = 6.6×10-34 J-s)

[A] 4.16×10-34 J-s
[B] 3.32×10-34J-s
[C] 1.05×10-34 J-s
[D] 2.08×10-34 J-s

The concept of stationary orbits was proposed by

[A] Neil Bohr
[B] J.J. Thomson
[C] Rutherford
[D] I. Newton

The ratio of the speed of the electrons in the ground state of hydrogen to the speed of light in vacuum is

[A] \( \frac{1}{2}\)

[B] \( \frac{2}{137}\)

[C] \( \frac{1}{137}\)

[D] \( \frac{1}{237}\)

The ionisation potential of H-atom is 13.6 V. When it is excited from ground state by monochromatic radiations of 970.6 Å, the number of emission lines will be (according to Bohr’s theory [A] 10
[B] 3
[C] 6
[D] 4

Excitation energy of a hydrogen like ion in its first excitation state is 40.8 eV. Energy needed to remove the electron from the ion in ground state is

[A] 54.4 eV
[B] 13.6 eV
[C] 40.8 eV
[D] 27.2 eV

In Bohr’s model, the atomic radius of the first orbit is r0 then the radius of the third orbit is

[A] r0/9
[B] r0
[C] 9r0
[D] 3r0

The frequency of Kα, Kβ and Lλ X-rays of material are γ1 γ2 and γ3 respectively. Which of the following relations holds good [A] \( γ_2=\sqrt{γ_1γ_3}\)

[B] \( γ_3= \sqrt{γ_1γ_2}\)

[C] \( γ_2= \frac{γ1+γ3}{2}\)

[D] \( γ_2=γ_1+γ_3 \)

When the electron in hydrogen atom jumps from the second orbit to the first orbit, the wavelength of the radiation emitted is λ When the electron jumps from the third to the first orbit, [A] \( \frac{9}{4}\)λ

[B] \( \frac{4}{9}\)λ

[C] \( \frac{27}{32}\)λ

[D] \( \frac{32}{27}\)λ

The ground state energy of hydrogen atom is – 1 3. 6eV.The kinetic energy of the electron in this state is

[A] 1.85eV
[B] 13.6 eV
[C] 6.8 eV
[D] 3.4 eV

Atomic hydrogen is excited from the ground state to the nth state. The number of lines in the emission spectrum will be

[A] \( \frac{n(n+1)}{2}\)
[B] \( \frac{n(n-1)}{2}\)

[C] \( \frac{(n-1)^2}{2}\)

[D] \( \frac{(n+1)^2}{2}\)

The difference in angular momentum associated with the electron in the two successive orbits of hydrogen atom is

[A] \( \frac{h}{π}\)

[B] \(\frac{h}{2π}\)

[C] \( \frac{h}{2}\)

[D] \((n-1)\frac{h}{2π}\)

The ratio of the largest to shortest wavelengths in Balmer series of hydrogen spectra is

[A] \( \frac{25}{9}\)
[B] \( \frac{17}{6}\)
[C] \(\frac{9}{5}\)
[D] \(\frac{5}{4}\)

In hydrogen atom, if the difference in the energy of the electron in n = 2 and n = 3 orbits is E, the ionization energy of hydrogen atom is
[A] 13. 2E
[B] 7.2E
[C] 5.6E
[D] 3.2E1

Which of the following is not correct in Bohr model of hydrogen atom?

[A] The radius of nth orbit is proportional to n2
[B] The total energy of electron in n th orbit is proportional ton
[C] The angular momentum of an electron in an orbit is an integral multiple of\( \frac{h}{2π} \)
[D] The magnitude of the potential energy of an electron in any orbit is greater than its kinetic energy

If ω is the speed of electron in the nth orbit hydrogen atom, then

[A] ω ∝ n1/2
[B] ω ∝ \(\frac{1}{n}\)
[C] ω ∝ \(\frac{1}{n^2}\)
[D] ω ∝\(\frac{1}{n^3}\)