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A photon of energy 8 eV is incident on a...

A photon of energy `8 eV` is incident on a metal surface of threshold frequency `1.6 xx 10^(15) Hz`, then the maximum kinetic energy of photoelectrons emitted is `( h = 6.6 xx 10^(-34) Js)`

A

`4.8 eV`

B

`2.4 eV`

C

`1.4 eV`

D

`0.8 eV`

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The correct Answer is:
To find the maximum kinetic energy of photoelectrons emitted when a photon of energy \(8 \, \text{eV}\) is incident on a metal surface with a threshold frequency of \(1.6 \times 10^{15} \, \text{Hz}\), we can follow these steps: ### Step 1: Calculate the Work Function (\(\phi\)) The work function (\(\phi\)) can be calculated using the formula: \[ \phi = h \nu_0 \] where: - \(h\) is Planck's constant (\(6.6 \times 10^{-34} \, \text{Js}\)) - \(\nu_0\) is the threshold frequency (\(1.6 \times 10^{15} \, \text{Hz}\)) Substituting the values: \[ \phi = (6.6 \times 10^{-34} \, \text{Js}) \times (1.6 \times 10^{15} \, \text{Hz}) \] ### Step 2: Calculate \(\phi\) in Joules Calculating the above expression: \[ \phi = 6.6 \times 1.6 \times 10^{-34 + 15} = 10.56 \times 10^{-19} \, \text{J} \] Now, converting this energy from Joules to electron volts (1 eV = \(1.6 \times 10^{-19} \, \text{J}\)): \[ \phi = \frac{10.56 \times 10^{-19}}{1.6 \times 10^{-19}} \approx 6.6 \, \text{eV} \] ### Step 3: Calculate the Maximum Kinetic Energy (\(K_{\text{max}}\)) Using Einstein's photoelectric equation: \[ K_{\text{max}} = E - \phi \] where: - \(E\) is the energy of the incident photon (\(8 \, \text{eV}\)) - \(\phi\) is the work function we calculated (\(6.6 \, \text{eV}\)) Substituting the values: \[ K_{\text{max}} = 8 \, \text{eV} - 6.6 \, \text{eV} = 1.4 \, \text{eV} \] ### Final Answer The maximum kinetic energy of the emitted photoelectrons is: \[ K_{\text{max}} = 1.4 \, \text{eV} \] ---

To find the maximum kinetic energy of photoelectrons emitted when a photon of energy \(8 \, \text{eV}\) is incident on a metal surface with a threshold frequency of \(1.6 \times 10^{15} \, \text{Hz}\), we can follow these steps: ### Step 1: Calculate the Work Function (\(\phi\)) The work function (\(\phi\)) can be calculated using the formula: \[ \phi = h \nu_0 \] where: ...
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