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  • Consider a thin target (10 minus 2m square, 10 minus 3m thickness) of sodium, which produces a photocurrent of 100 mu A when a light of intensity 100 W/m2 (\lambda = 660nm) falls on it. Find the probability that a photoelectron is produced when a photon

Consider a thin target (10–2m square, 10–3m thickness) of sodium, which produces a photocurrent of 100 \mu A when a light of intensity 100W/m2 (\lambda = 660nm) falls on it. Find the probability that a photoelectron is produced when a photon strikes a sodium atom. [Take density of Na = 0.97 kg/m3].

 

Answers (1)

Area (A)=10-2 cm2=10-4m2

thickness (t)=10-3m

photo current (i)=100*10-6=10-4A

Intensity (I)=100 W/m2

wavelength (\lambda)=660 nm=660*10-9m

density (ρNa)=0.97 kg/m3

Avogadro's Number=6*1026Kg atom

Volume of target (V)=A*d=10-4*10-3=10-7m3

MNa (6*1026 atoms of Na)=23 kg

VNa (6*1026 atoms of Na) =

\frac{23}{0.97}m^{3}

NNa=

\frac{10^{-7}}{\frac{\frac{23}{0.97}}{6*10^{26}}}=2.53*10^{18}

Energy of photon=\frac{hc}{\lambda}

Total Energy=\frac{nhc}{\lambda}=IA

n=\frac{nA\lambda}{hc}=3.3*10^{16}\\\\ N=n*N_{Na}*p\\ i=Ne=n*N_{Na}*p*e\\ 10^{-4}=33*10^{16}*2.53*10^{18}*1.6*10^{-19}*p\\ p=7.48*10^{-21}

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