The energy of photon E = \(\frac { hc }{ \lambda } \) Joule
=\(\frac { hc }{ e\lambda } \) eV
=\(\frac { 6.63\times { 10 }^{ -34 }\times 3\times 10^{ 8 } }{ 1.6\times 10^{ -19 }\times 3.3\times 10^{ -7 } } \)eV
= 3.75 eV
Since W_O of M_O is greater than E,
∴ M_O will not give photoemission.

de Broglie wavelength associated with electron
\({ \lambda }_{ e }=\frac { h }{ \sqrt { 2mE_{ e } } } \Rightarrow { E }_{ e }=\frac { { h }^{ 2 } }{ 2m{ \lambda }_{ e }^{ 2 } } \)        ......(1)
Also, the wavelength of a photon of energy E_ph is
E_ph = \(\frac { hc }{ { \lambda }_{ ph } } \Rightarrow { E }_{ ph }^{ 2 }=\frac { { h }^{ 2 }{ c }^{ 2 } }{ { \lambda }_{ ph }^{ 2 } } \)        ......(2)
Given E_e = E_ph = E (say) = 100 eV    ......(3)
Dividing (2) by (1) and using (3), we get
E= \(\frac { { h }^{ 2 }{ c }^{ 2 }/{ \lambda }_{ ph }^{ 2 } }{ { h }^{ 2 }/2m{ \lambda }_{ e }^{ 2 } } \) or E = \(\frac { 2mc^{ 2 }{ \lambda }_{ e }^{ 2 } }{ { \lambda }_{ ph }^{ 2 } } \)

K.E.= \(\frac{1}{2}mv^2=qV or\)
\(v=\sqrt { \frac { 2qV }{ m } } \)
de Broglie wavelength, \(\lambda =\frac { h }{ mv } \)
\(=\frac { h }{ m\sqrt { \frac { 2qV }{ m } } } =\frac { h }{ \sqrt { 2mqV } } \)
For the same potential difference
\(\frac { { \lambda }_{ \alpha } }{ { \lambda }_{ p } } =\sqrt { \frac { { m }_{ p }{ q }_{ p } }{ { m }_{ \alpha }{ q }_{ \alpha } } } =\sqrt { \frac { { m }_{ p }e }{ { 4m }_{ p }2e } } \)
\(=\frac { 1 }{ 2\sqrt { 2 } } \)

Given λ = 589 nm = 5.89 x 10^-7 m
The de Broglie wavelength \(\lambda =\frac { h }{ p } =\frac { h }{ \sqrt { 2m{ E }_{ k } } } \Rightarrow { \lambda }^{ 2 }=\frac { { h }^{ 2 } }{ 2m{ E }_{ k } } \)
Kinetic energy \({ E }_{ k }=\frac { { h }^{ 2 } }{ 2m{ E }_{ k } } \)
(a) For electron \({ E }_{ k }=\frac { { h }^{ 2 } }{ 2m{ E }_{ k } } \)
\({ E }_{ k }=\frac { { (6.63\times 10 }^{ -34 })^{ 2 } }{ 2\times 9.1\times { 10 }^{ -31 }\times { ({ 5.89\times 10 }^{ -7 }) }^{ 2 } } \)
= 6.96 x 10^-25J
b) For neutron m = 1.67 x 10^-27 kg
\({ E }_{ k }=\frac { { (6.63\times 10 }^{ -34 })^{ 2 } }{ 2\times 1.67\times { 10 }^{ -31 }\times { ({ 5.89\times 10 }^{ -7 }) }^{ 2 } } \)
= 3.79 x1 0^-28J