Dual Nature Of Radiation And Matter Ques 17
17. An ionization chamber with parallel conducting plates as anode and cathode has $5 \times 10^{7}$ electrons and the same number of singly charged positive ions per $cm^{3}$. The electrons are moving towards the anode with velocity $0.4$ $ m / s$. The current density from anode to cathode is $4 $ $\mu A$ / $m^{2}$. The velocity of positive ions moving towards cathode is
[1992]
(a) $0.4$ $ m / s$
(b) $1.6 $ $m / s$
(c) zero
(d) $0.1$ $ m / s$
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Answer:
Correct Answer: 17.(d)
Solution:
- (d) Current $=I_e+I_p$
$I_e$ and $I_p$ are current due to electrons and positively charged ions.
$I=n e A V_d$
where,
$ n=5 \times 10^{7} / cm^{3}= 5 \times 10^{7} \times 10^{6} / m^{3} $
$ =5 \times 10^{13} / m^{3}$
$I_e=5 \times 10^{13} \times 1.6 \times 10^{-19} \times A \times 0.4$
$I_p=5 \times 10^{13} \times 1.6 \times 10^{-19} \times A \times v$
$I=I_e+I_p\quad $ (from equation (i))
$=5 \times 10^{13} \times 1.6 \times 10^{-19} \times A(v+0.4)$
Given, $I / A=4 \times 10^{-6} $ $A / m^{2}$
$4 \times 10^{-6} \times A=5 \times 10^{-6} \times 1.6 \times A(v+0.4)$
$\frac{4}{8}=v+0.4 \Rightarrow 0.5=v+0.4 \Rightarrow v=0.1 $ $m / s$
BETA
