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

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

[JEE Main 2024, 5 Apr (Shift 1)]

a

\({10}^{19}\)

b

\({10}^{36}\)

c

\({10}^{29}\)

d

\({10}^{39}\)

✓ Correct answer: d)

\({10}^{39}\)

Explanation

key concept= Columb's low + Law of gravitation

\({F}_{e}=\frac{k{r}_{1}{r}_{2}}{{r}^{2}}=\frac{9\times {10}^{9}\times {\left(1.6\times {10}^{-19}\right)}^{2}}{{r}^{2}}\)

\({F}_{g}=\frac{G{m}_{1}{m}_{2}}{{r}^{2}}=\frac{6.67\times {10}^{-11}\times 9.1\times {10}^{-31}\times 1.67\times {10}^{-27}}{{r}^{2}}\)

\(∴\frac{{\mathrm{F}}_{\mathrm{e}}}{{\mathrm{F}}_{\mathrm{g}}}=2.2\times {10}^{39}\)

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