Semiconducting Devices Question 61
Question: A metallic surface with work function of 2 eV, on heating to a temperature of 800 K gives an emission current of 1 mA. If another metallic surface having the same surface area, same emission constant but work function 4 eV is heated to a temperature of 1600 K, then the emission current will be
Options:
A) 1 mA
B) 2 mA
C) 4 mA
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
The emission current $ i=AT^{2}S{{e}^{-\varphi /kT}} $
For the two surfaces A1 = A2, S1 = S2, T1 = 800 K,
$ T _{2}=1600K,{\varphi _{1}}/T _{1}={\varphi _{2}}/T _{2} $
Therefore , $ \frac{i _{2}}{i _{1}}={{( \frac{T _{2}}{T _{1}} )}^{2}} $ = (2)2 = 4
Therefore $ i _{2}=4i _{1}=4mA.
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