How many times does light travel faster in vacuum than an electron in Bohr first orbit of hydrogen atom?

13.7

times

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67

times

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137

times

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97

times

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Solution

The correct option is D $137$ times
Velocity of electron in $n^{t h}$ orbit = $V_{0} \frac{z}{n}$ , according to Bohr model.
where $V_{0} = 2.18 \times 10^{6} m / s$
For hydrogen's first orbit , $z = 1, n = 1$
Speed of light = $3 \times 10^{8} m / s$
Let $3 \times 10^{8} = x (2.16 \times 10^{6})$
$⟹ x = 137$
Speed of light is 137 times faster.

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How many times does light travel faster in vacuum than an electron in Bohr first orbit of hydrogen atom?

The correct option is D 137 timesVelocity of electron in nth orbit = V0zn , according to Bohr model.where V0=2.18×106m/sFor hydrogen's first orbit , z=1,n=1Speed of light =3×108m/sLet 3×108=x(2.16×106)⟹x=137Speed of light is 137 times faster.