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A current of $80 μA$ flows in the filament of an X-ray tube. How many electrons are crossing a cross-section of filament per second? Given charge on an electron $= 1.6 \times 10^{- 19} C$ .

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5 \times 10^{4}

5 \times 10^{8}

5 \times 10^{10}

5 \times 10^{14}

answer is D.

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Detailed Solution

5 \times 10^{14}

electrons are crossing a cross-section of filament per second.
Given data in problem
Curent,

I = 80 μA

And

80 μA

it can written as

80 \times 10^{- 6} A

Taking time as 1 sec, Charge

Q = current \times time

\Rightarrow Q = 80 \times 10^{- 6} A

And, the charge of an electron,

e = 1.6 \times 10^{- 19} C

By using the formula

Q = ne

, where

Q

is charge,

e

is charge of an electron and

n

is number electron

80 \times 10^{- 6} = n \times 1.6 \times 10^{- 19}

\Rightarrow n = \frac{80 \times 10^{- 6}}{1.6 \times 10^{- 19}}

\Rightarrow n = \frac{80 \times 10^{19}}{1.6 \times 10^{6}}

\Rightarrow n = \frac{8 \times 10^{15}}{16}

\Rightarrow n = 0.5 \times 10^{15}

\Rightarrow n = \frac{5 \times 10^{15}}{10}

\Rightarrow n = 5 \times 10^{14}

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