NEET Atoms and Nuclei — Set 10

Question 1

What is the angular momentum of an electron in the $ n = 3 $ state of a hydrogen atom? (Use $ h = 6.6 \times 10^{-34} \, \text{J·s} $)

Accepted Answer

$ L = n \frac{h}{2\pi} $. For $ n = 3 $: $ L = 3 \times \frac{6.6 \times 10^{-34}}{2 \times 3.14} \approx 3.15 \times 10^{-34} \, \text{J·s} $.

Question 2

An electron in a hydrogen atom falls from $ n = 4 $ to $ n = 2 $. What is the energy of the emitted photon? (Use $ E_n = -\frac{13.6}{n^2} \, \text{eV} $)

Accepted Answer

$ E_4 = -\frac{13.6}{4^2} = -0.85 \, \text{eV} $, $ E_2 = -3.4 \, \text{eV} $. $ \Delta E = E_4 - E_2 = -0.85 - (-3.4) = 2.55 \, \text{eV} $.

Question 3

A hydrogen atom in the $ n = 3 $ state emits a photon and returns to the ground state. What is the maximum energy of the photon? (Use $ E_n = -\frac{13.6}{n^2} \, \text{eV} $)

Accepted Answer

$ E_3 = -1.51 \, \text{eV} $, $ E_1 = -13.6 \, \text{eV} $. $ \Delta E = 12.09 \, \text{eV} $.

NEET Physics: Atoms and Nuclei — Practice Set 10

Q1. What is the angular momentum of an electron in the \( n = 3 \) state of a hydrogen atom? (Use \( h = 6.6 \times 10^{-34} \, \text{J·s} \))

Q2. An electron in a hydrogen atom falls from \( n = 4 \) to \( n = 2 \). What is the energy of the emitted photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q3. A hydrogen atom in the \( n = 3 \) state emits a photon and returns to the ground state. What is the maximum energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q4. What is the frequency of revolution of an electron in the first orbit of a hydrogen atom if its speed is \( 2.2 \times 10^6 \, \text{m/s} \) and radius is \( 5.3 \times 10^{-11} \, \text{m} \)?

Q5. In Rutherford’s model, what is the ratio of the size of the nucleus to the size of the atom if the nuclear radius is \( 10^{-15} \, \text{m} \) and atomic radius is \( 10^{-10} \, \text{m} \)?

Q6. In Rutherford’s scattering experiment, what does the small number of alpha-particles undergoing head-on collisions suggest?

Q7. A hydrogen atom emits a photon when an electron drops from \( n = 5 \) to \( n = 2 \). What is the energy of the photon? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q8. What is the minimum energy required to excite a hydrogen atom from its ground state to the first excited state? (Use \( E_n = -\frac{13.6}{n^2} \, \text{eV} \))

Q9. What was the primary evidence from Rutherford’s alpha-particle scattering experiment that led to the nuclear model of the atom?

Q10. What is the speed of an electron in the \( n = 3 \) orbit of a hydrogen atom if its speed in \( n = 1 \) is \( 2.2 \times 10^6 \, \text{m/s} \)?