b
ઝડપ\(_{max} = 7 \times 10^5\ m/s\)

\({e^ - }\,\,\) ની ગતિ ઊર્જા  \( =   \frac{1}{2}\,\,m{v^2}\, = \,\,\frac{1}{2}\,\,m\, \times \,\,{(7\,\, \times \,\,{10^5})^2}\)

\( = \,\frac{1}{2}\,\, \times \,\,9.1\,\, \times \,\,{10^{ - 31}} \times \,\,49\,\, \times \,\,{10^{10}}\,\,\) \( = \,\,9.1\,\, \times \,\,{10^{ - 21}} \times \,\,49\,\, \times \,\,0.5\,\,J\)

આપેલ ઉત્સર્જાતી આવૃત્તિ \(= 8\times10^{14}Hz\)

 ફોટો ઈલેક્ટ્રીક સૂત્ર પરથી \(k_{max} = hv - hv_0\)

\(\rightarrow  hv_0 = hv - k_{max} = 6.6 \times 10^{-34}\)

\(\times 8 \times 10^{14} - 91 \times 49 \times 5 \times 10^{-23}\)

\(= [6.6 \times 8 \times 10^{-20} - 91 \times 49\)\(\times 5 \times 10^{-23}]\)

\(= 10^{-21} [66 \times 8 - 91 \times 49 \times 5 \times 10^{-2}]\)

\(= [528 -223] \times 10^{-21} = 6.6 \times 10^{-34}v_0\)

\({v_0} = \,\,\,\frac{{305}}{{6.6}}\,\, \times \,\,{10^{ - 21}} \times \,{10^{34}}\)

\( = \,\,\frac{{30.5}}{{6.6}}\,\, \times \,\,{10^{14}}\, = \,\,{v_0}\)

\( \Rightarrow \,\,4.64\,\, \times \,\,{10^{14}}\,Hz\)