Max velocity of emitted electron can be calculated using the equation:

\[
\frac{1}{2} m v_{\text{max}}^2 = K.E._{\text{max}} = E - W
\]

Where:
- \(m\) is the mass of the electron
- \(v_{\text{max}}\) is the maximum velocity of the emitted electron
- \(K.E._{\text{max}}\) is the maximum kinetic energy of the emitted electron
- \(E\) is the energy of the incident photon
- \(W\) is the work function of the metal plate

To find the maximum velocity, we need to calculate the maximum kinetic energy first.

1. Find the energy of the incident photon using the equation:

\[
E = \frac{hc}{\lambda}
\]

Where:
- \(h\) is the Planck's constant (\(6.626 \times 10^{-34}\) J.s)
- \(c\) is the speed of light (\(3 \times 10^8\) m/s)
- \(\lambda\) is the wavelength of the incident light (200 nm)

Substituting the values:

\[
E = \frac{(6.626 \times 10^{-34} \, \text{J.s})(3 \times 10^8 \, \text{m/s})}{200 \times 10^{-9} \, \text{m}}
\]

Simplifying:

\[
E = 9.939 \times 10^{-19} \, \text{J}
\]

2. Calculate the maximum kinetic energy using the equation:

\[
K.E._{\text{max}} = E - W
\]

Substituting the values:

\[
K.E._{\text{max}} = (9.939 \times 10^{-19} \, \text{J}) - (1.21 \, \text{eV})(1.6 \times 10^{-19} \, \text{J/eV})
\]

Simplifying:

\[
K.E._{\text{max}} = 9.939 \times 10^{-19} \, \text{J} - 1.936 \times 10^{-19} \, \text{J}
\]

\[
K.E._{\text{max}} = 8.003 \times 10^{-19} \, \text{J}
\]

3. Finally, calculate the maximum velocity using the equation:

\[
\frac{1}{2} m v_{\text{max}}^2 = K.E._{\text{max}}
\]

Simplifying:

\[
v_{\text{max}}^2 = \frac{2K.E._{\text{max}}}{m}
\]

Substituting the values:

\[
v_{\text{max}}^2 = \frac{2(8.003 \times 10^{-19} \, \text{J})}{9.11 \times 10^{-31} \, \text{kg}}
\]

Simplifying:

\[
v_{\text{max}}^2 = 1.755 \times 10^{12} \, \text{m}^2/\text{s}^2
\]

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