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11. Dual nature of radiation and matter — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics11. Dual nature of radiation and matter1 Mark
MCQ
While doing his experiment, Millikan one day observed the following charges on a single drop

$(i)$ $6.563 \times {10^{ - 19}}C$       $  (ii)$ $8.204 \times {10^{ - 19}}C$

$(iii)$ $11.50 \times {10^{ - 19}}C$       $ (iv)$ $13.13 \times {10^{ - 19}}C$

$(v)$ $16.48 \times {10^{ - 19}}C$       $ (vi)$ $18.09 \times {10^{ - 19}}C$

From this data the value of the elementary charge $(e)$ was found to be

  • ✓
    $1.641 \times {10^{ - 19}}C$
  • B
    $1.630 \times {10^{ - 19}}C$
  • C
    $1.648 \times {10^{ - 19}}C$
  • D
    $1.602 \times {10^{ - 19}}C$
✓

Answer

Correct option: A.
$1.641 \times {10^{ - 19}}C$
a
(a) Any charge in the universe is given by

$q = ne \Rightarrow e = \frac{q}{n}$ (where $n$ is an integer)

${q_1}:{q_2}:{q_3}:{q_4}:{q_5}:{q_6}::{n_1}:{n_2}:{n_3}:{n_4}:{n_5}:{n_6}$

$6.563:8.204:11.5:13.13:16.48:18.09$$::{n_1}:{n_2}:{n_3}:{n_4}:{n_5}:{n_6}$

Divide by $6.563$

$1:1.25:1.75:2.0:2.5:2.75$$::{n_1}:{n_2}:{n_3}:{n_4}:{n_5}:{n_6}$

Multiplied by $4$

$4:5:7:8:10:11$$::{n_1}:{n_2}:{n_3}:{n_4}:{n_5}:{n_6}$

$e = \frac{{{q_1} + {q_2} + {q_3} + {q_4} + {q_5} + {q_6}}}{{{n_1} + {n_2} + {n_3} + {n_4} + {n_5} + {n_6}}} = \frac{{73.967 \times {{10}^{ - 19}}}}{{45}}$

$ = 1.641 \times {10^{ - 19}}C$

(Note : If you take $45.0743$ in place of $45$ , you will get the exact value)

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