NEET Structure of Atom — Set 7

Question 1

What is the radius ratio of the third orbit to the first orbit in a hydrogen atom?

Accepted Answer

Radius $ r_n = r_1 \times n^2 $. For $ n = 3 $, $ r_3 = r_1 \times 9 $. Ratio $ \frac{r_3}{r_1} = 9 $.

Question 2

The kinetic energy of a photoelectron is $ 1.5 \times 10^{-19} \, \text{J} $ when light of wavelength $ 400 \, \text{nm} $ is used. What is the work function? ($ h = 6.626 \times 10^{-34} \, \text{J s} $, $ c = 3.0 \times 10^8 \, \text{m s}^{-1} $)

Accepted Answer

Photon energy $ E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3.0 \times 10^8}{400 \times 10^{-9}} = 4.9695 \times 10^{-19} \, \text{J} $. $ W_0 = E - KE = 4.9695 \times 10^{-19} - 1.5 \times 10^{-19} = 3.4695 \times 10^{-19} \, \text{J} $.

Question 3

The energy of a photon is given by $ E = h v $, where $ h = 6.626 \times 10^{-34} \, \text{J s} $ and frequency $ v = 4.0 \times 10^{14} \, \text{Hz} $. Calculate the energy in joules.

Accepted Answer

Energy $ E = h v = 6.626 \times 10^{-34} \times 4.0 \times 10^{14} = 2.6504 \times 10^{-19} \, \text{J} $.

NEET Chemistry: Structure of Atom — Practice Set 7

Q1. What is the radius ratio of the third orbit to the first orbit in a hydrogen atom?

Q2. The kinetic energy of a photoelectron is \( 1.5 \times 10^{-19} \, \text{J} \) when light of wavelength \( 400 \, \text{nm} \) is used. What is the work function? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( c = 3.0 \times 10^8 \, \text{m s}^{-1} \))

Q3. The energy of a photon is given by \( E = h v \), where \( h = 6.626 \times 10^{-34} \, \text{J s} \) and frequency \( v = 4.0 \times 10^{14} \, \text{Hz} \). Calculate the energy in joules.

Q4. How many possible values of \( m_s \) are there for an electron with \( n = 4, l = 2, m_l = 1 \)?

Q5. An electron jumps from \( n = 4 \) to \( n = 1 \) in a hydrogen atom. What is the energy of the emitted photon? (\( E_1 = -2.18 \times 10^{-18} \, \text{J} \))

Q6. A neutron has a de Broglie wavelength of \( 3.0 \times 10^{-12} \, \text{m} \). What is its kinetic energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_n = 1.67 \times 10^{-27} \, \text{kg} \))

Q7. The radius of the first orbit of \( \text{Li}^{2+} \) is \( 1.763 \times 10^{-11} \, \text{m} \). What is the kinetic energy of an electron in the third orbit? (\( v_1 \) for H = \( 2.19 \times 10^6 \, \text{m s}^{-1} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q8. An alpha particle and a proton have the same kinetic energy. What is the ratio of their de Broglie wavelengths? (\( m_p = 1.67 \times 10^{-27} \, \text{kg} \), \( m_{\alpha} = 6.64 \times 10^{-27} \, \text{kg} \))

Q9. An electron in \( \text{Li}^{2+} \) has a de Broglie wavelength of \( 2.21 \times 10^{-10} \, \text{m} \) in the second orbit. What is its kinetic energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( m_e = 9.1 \times 10^{-31} \, \text{kg} \))

Q10. The angular momentum of an electron in the sixth orbit of a hydrogen atom is \( 6.33 \times 10^{-34} \, \text{J s} \). What is its energy? (\( h = 6.626 \times 10^{-34} \, \text{J s} \), \( E_1 = -2.18 \times 10^{-18} \, \text{J} \))