Question

The work function of a metal is 2 eV. What is the threshold frequency for the photoelectric emission? (Take Planck's constant $ h = 6.63 \times 10^{-34} \, \text{Js} $, $ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} $)

• A. \(4.8 \times 10^{14} \, \text{Hz}\)
• B. \(5.2 \times 10^{14} \, \text{Hz}\)
• C. \(6.2 \times 10^{14} \, \text{Hz}\)
• D. \(7.4 \times 10^{14} \, \text{Hz}\)

Hint:

To find the threshold frequency, always convert the work function from eV to joules before using \( f = \frac{E}{h} \).

Answer 1

The Correct Option is A

To determine the threshold frequency \( f_0 \) for photoelectric emission, we use the equation relating work function (ϕ) and Planck's constant (h):

\( ϕ = h \cdot f_0 \)

Given:

• Work function \( ϕ = 2 \, \text{eV} = 2 \times 1.6 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-19} \, \text{J} \)
• Planck's constant \( h = 6.63 \times 10^{-34} \, \text{Js} \)

Substitute these values into the equation:

\( 3.2 \times 10^{-19} = 6.63 \times 10^{-34} \times f_0 \)

Solve for \( f_0 \):

\( f_0 = \frac{3.2 \times 10^{-19}}{6.63 \times 10^{-34}} \)

\( f_0 = 4.8 \times 10^{14} \, \text{Hz} \)

Thus, the threshold frequency for the photoelectric emission is \( 4.8 \times 10^{14} \, \text{Hz} \).

Answer 2

The threshold frequency for the photoelectric emission can be calculated using the relation between the work function (\(W\)) and the frequency (\(f\)): \[ W = hf \] where \(W\) = work function in Joules, \(h\) = Planck's constant (\(6.63 \times 10^{-34} \, \text{Js}\)), \(f\) = threshold frequency. Given that the work function is \(2 \, \text{eV}\), we first convert it to Joules: \[ 2 \, \text{eV} = 2 \times 1.6 \times 10^{-19} \, \text{J} = 3.2 \times 10^{-19} \, \text{J} \] Now, we rearrange the formula to solve for the threshold frequency (\(f\)): \[ f = \frac{W}{h} = \frac{3.2 \times 10^{-19}}{6.63 \times 10^{-34}} \, \text{Hz} \] Calculating this gives: \[ f \approx 4.82 \times 10^{14} \, \text{Hz} \] Rounding to two significant digits, we have the threshold frequency: \[ f = 4.8 \times 10^{14} \, \text{Hz} \] This matches the option \(4.8 \times 10^{14} \, \text{Hz}\). Thus, the correct threshold frequency is \(4.8 \times 10^{14} \, \text{Hz}\).