The work function of cesium is 2.14 eV. The threshold frequency of cesium 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 1: Understand the Work Function
The work function (Φ) is the minimum energy required to remove an electron from a material. For cesium, the work function is given as 2.14 eV.

### Step 2: Convert Work Function to Joules
Since the work function is given in electron volts (eV), we need to convert it to joules (J) for our calculations. The conversion factor is:
1 eV = 1.6 × 10^(-19) J.

So, we calculate:
\[ \Phi = 2.14 \, \text{eV} \times 1.6 \times 10^{-19} \, \text{J/eV} = 3.424 \times 10^{-19} \, \text{J} \]

### Step 3: Use the Formula for Threshold Frequency
The threshold frequency (ν₀) can be calculated using the formula:
\[ \Phi = h \nu_0 \]
where \( h \) is Planck's constant, approximately \( 6.626 \times 10^{-34} \, \text{J s} \).

Rearranging the formula gives us:
\[ \nu_0 = \frac{\Phi}{h} \]

### Step 4: Substitute the Values
Now, substituting the values we have:
\[ \nu_0 = \frac{3.424 \times 10^{-19} \, \text{J}}{6.626 \times 10^{-34} \, \text{J s}} \]

### Step 5: Calculate the Threshold Frequency
Performing the division:
\[ \nu_0 = 5.16 \times 10^{14} \, \text{Hz} \]

### Step 6: Final Result
Thus, the threshold frequency of cesium is approximately:
\[ \nu_0 \approx 5.16 \times 10^{14} \, \text{Hz} \]