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QNEET-2023-Ph-251: NEET 2023 Physics - Class 12 NEET-2023-Ph-251 Solution: The radius of inner most orbit of hydrogen atom is \(5.3…
The radius of inner most orbit of hydrogen atom is . What is the radius of third allowed orbit of hydrogen atom?
Multiple Choice Options
- A 1.06 A o _
- B 1.59 A o _
- C 4.77 A o _
- D 0.53 A o _
Step-by-Step Verified Solution
The formula to calculate the radius of the nth orbit in a hydrogen atom is given by the equation:
r n = r 0 _ n 2
where,
r n is the radius of the nth orbit,
r 0 is the radius of the innermost orbit (known as the Bohr radius), and
n is the orbit number.
Given that the radius of the innermost orbit ( r 0 ) is 5.3 _ 10 _ 11 m or equivalently 0.53 A o , and we're interested in finding the radius of the third orbit ( n = 3 ).
So,
r 3 = 0.53 _ ( 3 ) 2 A o
r 3 = 0.53 _ 9 A o
r 3 = 4.77 A o
Therefore, the radius of the third allowed orbit of the hydrogen atom is 4.77 A o .