\(P=4 \ \mathrm{cal} \mathrm{} \mathrm{cm}^{-2} \mathrm{~min}^{-1}=4 \times 4.2=16.8 \mathrm{~J} \mathrm{~cm}^{-2} \mathrm{~min}^{-1} \)
\(E=\frac{h c}{\lambda}=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{5500 \times 10^{-10}}=3.6 \times 10^{-19} \mathrm{~J} \)
\(n=\frac{E}{hv}=\frac{16.8}{3.6 \times 10^{-19}}=4.67 \times 10^{19} \)
\(n=4.67 \times 10^{19} \)  per cm² per minute.

V = 81 V
∴ K = eV = 1.6 x 10^-19 x 81 = 1.296 x 10^-17 = 1.3 x 10^-17 J
\({ V }=\sqrt \frac {2K}{m}\sqrt { \cfrac { 2\times 1.3\times { 10 }^{ -17 } }{ 9.1\times { 10 }^{ -31 } } } =5.345 \times 10^6 ms^{-1} \) 
v = 5.345 x 10⁶ m s^-1, K = 1.3 x 10^-17 J

\(\lambda=6000Å=6000 \times 10^{-10} \mathrm{~m} ; \mathrm{V}=0.8 \mathrm{v} \)
\(\mathrm{k} \cdot \mathrm{E}=\mathrm{hv}-\phi \)
\(\mathrm{eV}_o=\mathrm{hv}-\phi=\frac{\mathrm{hc}}{\lambda}-\phi \)
\((i) v=\frac{c}{\lambda}=\frac{3 \times 10^{8}}{6000 \times 10^{-10}}=5 \times 10^{14} \mathrm{~Hz} \)
\((ii)\ \mathrm{E}=\frac{\mathrm{hc}}{\lambda}=\frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{6000 \times 10^{-10}}=3.313 \times 10^{-19} J\)
\(\mathrm{E}=\frac{3.313 \times 10^{-19}}{1.6 \times 10^{-19}}=2.07 \mathrm{eV} \)
\((iii) \ \mathrm{E}=\mathrm{hv}-\mathrm{W}\Rightarrow\mathrm{W}=\mathrm{h} v-\mathrm{E} \)
\(\mathrm{E}=\mathrm{eV_o}=1.6 \times 10^{-19} \times 0.8=1.2 8 \times10^{-19}J\)
\(\mathrm{hv}=6.626 \times 10^{-34} \times 5 \times 10^{14}=3.313 \times 10^{-19}J \)
\(\mathrm{~W}=\frac{(3.313-1.28) \times 10^{-19}}{1.6 \times 10^{-19}}=1.270 \mathrm{eV} \)
W = 1.27 eV
\((iv) \ \mathrm{W}=\mathrm{h} \mathrm{v}_{0} \)
\(v_{0}=\frac{W}{h}=\frac{2.033 \times 10^{-19}}{6.626 \times 10^{-34}}=3.07 \times 10^{14} \mathrm{~Hz} \)
\((v)\ \mathrm{E}=\mathrm{eV}_o=\frac{0.8 \times 1.6 \times 10^{-19}}{1.6 \times 10^{-19}}=\mathbf{0 . 8} \mathrm{eV}\)

\(\lambda=4000 \stackrel{o}A=4000 \times 10^{-10} \mathrm{~m} \)
\(\lambda=\frac{\mathrm{h}}{\mathrm{mv}}\Rightarrow \mathrm{v }=\frac{\mathrm{h}}{\mathrm{m\lambda}}=\frac{6.626 \times 10^{-34}}{9.1 \times 10^{-31} \times 4000 \times 10^{10}}=1820 \mathrm{~ms}^{-1} \)

λ = 5500 x 10^-10 m; P =150 W; Efficiency =12%
\({ E }=\cfrac { hc }{ { \lambda } } =\cfrac { 6.626\times { 10 }^{ -34 }\times 3 \times { 10 }^{ 8 } }{ 5500\times { 10 }^{ -10 } }=3.614 \times 10^{-19} J \)
\(n=\frac{E}{hv}=\cfrac { 150 }{ 3.614\times { 10 }^{ -19 } } =4.15 \times 10^{20}\times\frac{12}{100}\)
n = 4.98 x 10¹⁹s^-1