The threshold frequency for the ejection of electrons from potassium metal is `5.3xx10^(14) s^(-1)`. Will the photon of a radiation having energy `3.3xx10^(-19) J` exhibit photoelectric effect? `(h=6.626xx10^(-34) Js)`

Explanation

To determine whether the photon of radiation with energy \(3.3 \times 10^{-19} \, \text{J}\) will exhibit the photoelectric effect when interacting with potassium metal, we can follow these steps:

### Step 1: Calculate the Work Function
The work function \(W\) of a material can be calculated using the formula:
\[ W = h \nu_0 \]
where:
- \(h\) is Planck's constant (\(6.626 \times 10^{-34} \, \text{Js}\))
- \(\nu_0\) is the threshold frequency (\(5.3 \times 10^{14} \, \text{s}^{-1}\))

Substituting the values:
\[ W = (6.626 \times 10^{-34} \, \text{Js}) \times (5.3 \times 10^{14} \, \text{s}^{-1}) \]

### Step 2: Perform the Calculation
Calculating the work function:
\[ W = 6.626 \times 5.3 \times 10^{-34 + 14} = 35.1 \times 10^{-20} \, \text{J} = 3.51 \times 10^{-19} \, \text{J} \]

### Step 3: Compare Energy of the Photon with Work Function
Now, we compare the energy of the photon \(E\) with the work function \(W\):
- Energy of the photon \(E = 3.3 \times 10^{-19} \, \text{J}\)
- Work function \(W = 3.51 \times 10^{-19} \, \text{J}\)

### Step 4: Determine if Photoelectric Effect Occurs
To exhibit the photoelectric effect, the energy of the photon must be greater than or equal to the work function:
\[ E < W \quad \text{(since } 3.3 \times 10^{-19} \, \text{J} < 3.51 \times 10^{-19} \, \text{J}\text{)} \]

Since the energy of the photon is less than the work function, the photoelectric effect will not occur.

### Conclusion
The photon of radiation with energy \(3.3 \times 10^{-19} \, \text{J}\) will **not** exhibit the photoelectric effect on potassium metal.

---