What is the binding energy (in J/mol or KJ/mol) of an electron in a metal. Whose threshold frequency for photon electron is `2.5xx10^(14)s^(-1)` ?

Options

A. 99.38 KJ/mol
B. `1.66 xx10^(-19)` J/ mol
C. `2.75 xx10^(-43)` J/mol
D. `7.22xx10^(17)` kJ/mol

Answer

To determine the binding energy of an electron in a metal given the threshold frequency, we can follow these steps:

### Step 1: Identify the given values
- Threshold frequency (ν) = \(2.5 \times 10^{14} \, \text{s}^{-1}\)
- Planck's constant (h) = \(6.626 \times 10^{-34} \, \text{J s}\)

### Step 2: Calculate the work function (φ)
The work function (φ) can be calculated using the formula:
\[ \phi = h \nu \]
Substituting the values:
\[ \phi = (6.626 \times 10^{-34} \, \text{J s}) \times (2.5 \times 10^{14} \, \text{s}^{-1}) \]
Calculating this gives:
\[ \phi = 1.6565 \times 10^{-19} \, \text{J} \]

### Step 3: Convert the work function to kJ/mol
To convert the work function from joules to kilojoules per mole, we use Avogadro's number (\(N_A = 6.022 \times 10^{23} \, \text{mol}^{-1}\)):
\[ \text{Binding Energy (in J/mol)} = \phi \times N_A \]
Substituting the values:
\[ \text{Binding Energy} = (1.6565 \times 10^{-19} \, \text{J}) \times (6.022 \times 10^{23} \, \text{mol}^{-1}) \]
Calculating this gives:
\[ \text{Binding Energy} \approx 99.38 \, \text{kJ/mol} \]

### Final Answer
The binding energy of the electron in the metal is approximately **99.38 kJ/mol**.

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