In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of

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Solution

Q.
In hydrogen like system the ratio of coulombian force and gravitational force between an electron and a proton is in the order of [2024]

1 $10^{39}$

2 $10^{19}$

3 $10^{29}$

4 $10^{36}$

Ans.
(1)

$F_{e} = \frac{k Q_{1} Q_{2}}{r^{2}} = \frac{9 \times 10^{9} \times 1.6 \times 10^{- 19} \times 1.6 \times 10^{- 19}}{r^{2}}$

$F_{g} = \frac{G m_{1} m_{2}}{r^{2}} = \frac{6.67 \times 10^{- 11} \times 9.1 \times 10^{- 31} \times 1.6 \times 10^{- 27}}{r^{2}}$

$\frac{F_{e}}{F_{g}} ≅ 0.23 \times 10^{40} ≅ 2.3 \times 10^{39}$

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