A metal X has a work function value of 2.1 eV Will there be any photoelectric emission for light of wavelength `5,000Å` . Value nf h `=6.63 xx10^(-34) J s^(-1)`.

Answer

To determine whether there will be any photoelectric emission from metal X when exposed to light of wavelength 5000 Å, we can follow these steps:

### Step 1: Understand the Work Function
The work function (φ) of the metal is given as 2.1 eV. This is the minimum energy required to eject an electron from the surface of the metal.

### Step 2: Calculate the Energy of the Incident Light
The energy (E) of the incident light can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where:
- \( h \) is Planck's constant, \( 6.63 \times 10^{-34} \, \text{J s} \),
- \( c \) is the speed of light, \( 3 \times 10^8 \, \text{m/s} \),
- \( \lambda \) is the wavelength of the light in meters.

First, convert the wavelength from angstroms to meters:
\[ 5000 \, \text{Å} = 5000 \times 10^{-10} \, \text{m} = 5 \times 10^{-7} \, \text{m} \]

Now, substitute the values into the energy formula:
\[ E = \frac{(6.63 \times 10^{-34} \, \text{J s}) \times (3 \times 10^8 \, \text{m/s})}{5 \times 10^{-7} \, \text{m}} \]

### Step 3: Calculate the Energy in Joules
Calculating the above expression:
\[ E = \frac{(6.63 \times 3) \times 10^{-26}}{5} = \frac{19.89 \times 10^{-26}}{5} = 3.978 \times 10^{-26} \, \text{J} \]

### Step 4: Convert Energy from Joules to Electron Volts
To convert Joules to electron volts, use the conversion factor \( 1 \, \text{eV} = 1.6 \times 10^{-19} \, \text{J} \):
\[ E \, (\text{in eV}) = \frac{3.978 \times 10^{-26} \, \text{J}}{1.6 \times 10^{-19} \, \text{J/eV}} \approx 2.48 \, \text{eV} \]

### Step 5: Compare Incident Energy with Work Function
Now, compare the calculated energy of the incident light (2.48 eV) with the work function (2.1 eV):
- Incident Energy = 2.48 eV
- Work Function = 2.1 eV

Since \( 2.48 \, \text{eV} > 2.1 \, \text{eV} \), the incident energy is greater than the work function.

### Conclusion
Since the energy of the incident light is greater than the work function of the metal, photoelectric emission will occur.

### Final Answer
Yes, there will be photoelectric emission.

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