If the binding energy of electrons in a metal is 250 kJ `"mol"^(-1)` , what is the threshold frequency of the striking photons ?

Options

A. `4xx10^(15) sec^(-1)`
B. `3xx10^(12) sec^(-1)`
C. `5xx120^(10) sec^(-1)`
D. `6xx10^(14) sec^(-1)`

Answer

To find the threshold frequency of the striking photons given the binding energy of electrons in a metal, we can follow these steps:

### Step 1: Convert the binding energy from kJ/mol to J
The binding energy of electrons in the metal is given as 250 kJ/mol. We need to convert this to joules.

\[ \text{Binding Energy} = 250 \, \text{kJ/mol} = 250 \times 10^3 \, \text{J/mol} \]

### Step 2: Calculate the binding energy per electron
Since the binding energy is given per mole, we need to divide this value by Avogadro's number (approximately \(6.022 \times 10^{23}\) mol\(^{-1}\)) to find the binding energy for a single electron.

\[ \text{Binding Energy per electron} = \frac{250 \times 10^3 \, \text{J/mol}}{6.022 \times 10^{23} \, \text{mol}^{-1}} \]

Calculating this gives:

\[ \text{Binding Energy per electron} \approx 4.15 \times 10^{-19} \, \text{J} \]

### Step 3: Relate binding energy to threshold frequency
The binding energy of an electron can be expressed in terms of the threshold frequency (\(\nu_0\)) using the equation:

\[ E = h \nu_0 \]

Where \(E\) is the binding energy, and \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{J s}\)).

### Step 4: Solve for the threshold frequency (\(\nu_0\))
Rearranging the equation gives:

\[ \nu_0 = \frac{E}{h} \]

Substituting the values we have:

\[ \nu_0 = \frac{4.15 \times 10^{-19} \, \text{J}}{6.626 \times 10^{-34} \, \text{J s}} \]

Calculating this gives:

\[ \nu_0 \approx 6.26 \times 10^{14} \, \text{s}^{-1} \]

### Final Answer
The threshold frequency of the striking photons is approximately \(6.26 \times 10^{14} \, \text{s}^{-1}\).

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