Question

radius of 2nd orbit of H atom is R.radius of 3rd orbit will be

Answer 1

we know that radius of any orbit of hydrogen is given by 52.9 pm × n²

where pm is picometres = 10⁻¹² metres and n is the respective orbit

let us find the radius of second orbit = 52.9 pm × 2² = R

the radius of 3rd orbit = 52.9 pm × 3²

let us the multiply and divide the radius of 3rd orbit with 4

the radius of 3rd orbit = 52.9 pm × 4/4 × 3²

⇒ the radius of 3rd orbit = 52.9 pm × 2²/2² × 3²

but we know that 52.9 pm × 2² = R

⇒ the radius of 3rd orbit = R × 3² × 1/2²

⇒ the radius of 3rd orbit = 9R/4

⇒ if the radius of 2nd orbit of hydrogen atom is R then the radius of 3rd orbit of hydrogen orbit = 9R/4