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Question

The ratio of the speed of the electron in the ground state of a hydrogen atom to the speed of light is


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Solution

Speed of the electron in the ground state.

The speed of the electron in the ground state is the numeric value of the velocity of the electron in the 1st orbit. It is equal to 2.19×106m/s

Step 1: Given:

The electron is in the ground state, so n=1

Step 2: Formula Used:

The speed of revolving electron in nth state of hydrogen atom = v=e22nh0

Here e is charge on electron, n is state of electron, h is plank's constant, 0 is permeability free space.

Step 3: Calculating the speed of the electron in hydrogen ground state:

For ground state, n=1

v=(1.6×10-19)22(1)(6.6×10-34)(8.85×10-12)v=2.56×10-38116.82×10-46v=0.0219×108m/sor2.19×106m/s

Step 4: Calculating the ratio of the speed of the electron in hydrogen ground state to the speed of light:

Speed of light, c=3×108

Hence, The ratio of the speed of the electron in the ground state of a hydrogen atom to the speed of light is

vc=0.0219×1083×108vc=1137

Final Answer: The ratio of the speed of the electron in the ground state of a hydrogen atom to the speed of light is 1137


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