Question

The ratio of time periods in second orbit of hydrogen to third orbit of helium

Answer 1

Answer:

We know that,

$\red{\boxed{\rm T \;\;\alpha\;\;\dfrac{n^3}{Z^2} }}$

Time period is directly proportional to Orbit number

and inversely proportional to Atomic number

Where,

T = Time Period

n = Orbit

Z = Atomic Number

For Hydrogen

T₁ = Time Period of H

n₁ = 2

Z₁ = 1

For Helium

T₂ = Time Period He

n₂ = 3

Z₂ = 2

According to the question,

We are asked to find the ratio of Time Periods of Hydrogen and Helium

$\rm \implies \dfrac{T_1}{T_2}=$

Hence,

The Formula is,

$\blue{\boxed{\rm \dfrac{T_1}{T_2} = \dfrac{n_1^3}{n_2^3} \times \dfrac{Z_2^2}{Z_1^2} }}}}$

Therefore,

By Substituting the above values in the formula

We get,

$\green{\implies \rm \dfrac{T_1}{T_2} = \dfrac{2^3}{3^3} \times \dfrac{2^2}{1^2} }}}$

$\purple{\implies \rm \dfrac{T_1}{T_2} = \dfrac{8}{27} \times \dfrac{4}{1} }}}}}$

$\pink{\implies \rm \dfrac{T_1}{T_2} = \dfrac{32}{27}}}$

$\red{\boxed{\boxed{ \rm \dfrac{T_1}{T_2} = \dfrac{32}{27}}}}}$

Hence,

The ratio of time periods in second orbit of Hydrogen to third orbit of Helium is

$\huge{\green{{\implies \rm \dfrac{T_1}{T_2} = \dfrac{32}{27}}}}}$