What will be the maximum kinetic energy of the photoelectrons ejected from magnesium (for which the work -function W=3.7 eV) when irradiated by ultraviolet light of frequency `1.5xx10^15 s^(-1)`.

Explanation

To find the maximum kinetic energy of the photoelectrons ejected from magnesium when irradiated by ultraviolet light, we can follow these steps:

### Step 1: Understand the relationship between energy, work function, and kinetic energy
The maximum kinetic energy (K.E.) of the photoelectrons can be calculated using the equation:
\[ K.E. = E - W \]
where:
- \( E \) is the energy of the incident photons,
- \( W \) is the work function of the material.

### Step 2: Calculate the energy of the incident photons
The energy \( E \) of the photons can be calculated using the formula:
\[ E = h \nu \]
where:
- \( h \) is Planck's constant (\( 6.63 \times 10^{-34} \, \text{J s} \)),
- \( \nu \) is the frequency of the light (\( 1.5 \times 10^{15} \, \text{s}^{-1} \)).

### Step 3: Substitute the values into the energy equation
Substituting the values into the equation:
\[ E = (6.63 \times 10^{-34} \, \text{J s}) \times (1.5 \times 10^{15} \, \text{s}^{-1}) \]

### Step 4: Calculate the energy in joules
Calculating the above expression:
\[ E = 9.945 \times 10^{-19} \, \text{J} \]

### Step 5: Convert energy from joules to electron volts
To convert joules to electron volts, we use the conversion factor:
\[ 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \]
Thus,
\[ E = \frac{9.945 \times 10^{-19} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \]
Calculating this gives:
\[ E \approx 6.215625 \, \text{eV} \]

### Step 6: Substitute the work function value
Now, we know the work function \( W \) for magnesium is \( 3.7 \, \text{eV} \). We can substitute this value into our kinetic energy equation:
\[ K.E. = E - W \]
\[ K.E. = 6.215625 \, \text{eV} - 3.7 \, \text{eV} \]

### Step 7: Calculate the maximum kinetic energy
Calculating the above expression gives:
\[ K.E. = 2.515625 \, \text{eV} \]

### Final Answer
The maximum kinetic energy of the photoelectrons ejected from magnesium is approximately:
\[ K.E. \approx 2.52 \, \text{eV} \]

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