The work function of cesium is 2.14 eV. The threshold freqency of caesium is

Options

A. `5.16xx10^(19)Hz`
B. `5.16xx10^(16)Hz`
C. `5.16xx10^(18)Hz`
D. `5.16xx10^(14)Hz`

Explanation

To find the threshold frequency of cesium given its work function, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The work function (W) is related to the threshold frequency (ν₀) by the equation:
\[ W = h \nu_0 \]
where \( h \) is Planck's constant.

2. **Convert Work Function to Joules**: The work function is given in electron volts (eV). We need to convert this to joules. The conversion factor is:
\[ 1 \text{ eV} = 1.6 \times 10^{-19} \text{ J} \]
Therefore, for cesium:
\[ W = 2.14 \text{ eV} = 2.14 \times 1.6 \times 10^{-19} \text{ J} \]

3. **Calculate Work Function in Joules**:
\[ W = 2.14 \times 1.6 \times 10^{-19} = 3.424 \times 10^{-19} \text{ J} \]

4. **Use Planck's Constant**: The value of Planck's constant \( h \) is:
\[ h = 6.626 \times 10^{-34} \text{ J s} \]

5. **Rearrange the Equation to Find Threshold Frequency**:
\[ \nu_0 = \frac{W}{h} \]

6. **Substitute the Values**:
\[ \nu_0 = \frac{3.424 \times 10^{-19}}{6.626 \times 10^{-34}} \]

7. **Calculate Threshold Frequency**:
\[ \nu_0 \approx 5.16 \times 10^{14} \text{ Hz} \]

### Final Answer:
The threshold frequency of cesium is approximately \( 5.16 \times 10^{14} \text{ Hz} \).