NEET Dual Nature of Matter — Set 6

Question 1

A light source emits $ 5.0 \times 10^{15} $ photons per second with a power of $ 2.0 \, \text{mW} $. What is the energy of each photon in joules?

Accepted Answer

Power $ P = N \times E $. $ E = \frac{P}{N} = \frac{2.0 \times 10^{-3}}{5.0 \times 10^{15}} = 4.0 \times 10^{-19} \, \text{J} $.

Question 2

The threshold frequency of a metal is $ 6.0 \times 10^{14} \, \text{Hz} $. What is its work function in eV? (Take $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} $)

Accepted Answer

$ \phi_0 = h v_0 = 6.63 \times 10^{-34} \times 6.0 \times 10^{14} = 3.978 \times 10^{-19} \, \text{J} $. $ \phi_0 = \frac{3.978 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 2.486 \, \text{eV} $.

Question 3

The minimum wavelength of X-rays from a $ 15 \, \text{kV} $ tube is: (Take $ h = 6.63 \times 10^{-34} \, \text{J s} $, $ c = 3 \times 10^8 \, \text{m/s} $, $ e = 1.6 \times 10^{-19} \, \text{C} $)

Accepted Answer

$ E = e V = 1.6 \times 10^{-19} \times 15 \times 10^3 = 2.4 \times 10^{-15} \, \text{J} $. $ \lambda_{\min} = \frac{h c}{E} = \frac{6.63 \times 10^{-34} \times 3 \times 10^8}{2.4 \times 10^{-15}} \approx 8.2875 \times 10^{-11} \, \text{m} = 0.082875 \, \text{nm} $.

NEET Physics: Dual Nature of Matter — Practice Set 6

Q1. A light source emits \( 5.0 \times 10^{15} \) photons per second with a power of \( 2.0 \, \text{mW} \). What is the energy of each photon in joules?

Q2. The threshold frequency of a metal is \( 6.0 \times 10^{14} \, \text{Hz} \). What is its work function in eV? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))

Q3. The minimum wavelength of X-rays from a \( 15 \, \text{kV} \) tube is: (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q4. In the photoelectric effect, what does the saturation current depend on, assuming a fixed frequency above the threshold?

Q5. The maximum frequency of X-rays from a \( 35 \, \text{kV} \) tube is: (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q6. The stopping potential for photoelectrons emitted from a metal surface is \( 1.2 \, \text{V} \). What is the maximum kinetic energy of the photoelectrons in joules? (Take \( e = 1.6 \times 10^{-19} \, \text{C} \))

Q7. A light source emits \( 3.0 \times 10^{16} \) photons per second with a power of \( 9.0 \, \text{mW} \). What is the wavelength of the light? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( c = 3 \times 10^8 \, \text{m/s} \))

Q8. A light source emits photons of energy \( 3.0 \times 10^{-19} \, \text{J} \) at a rate of \( 4.0 \times 10^{15} \) photons per second. What is the power emitted?

Q9. A particle of mass \( 1.0 \times 10^{-28} \, \text{kg} \) has the same momentum as a photon of wavelength \( 600 \, \text{nm} \). What is its speed? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \))

Q10. The work function of a metal is \( 2.0 \, \text{eV} \). What is the threshold frequency for photoelectric emission from this metal? (Take \( h = 6.63 \times 10^{-34} \, \text{J s} \), \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \))