Question

Helium has atomic number Z=2 and mass number A=4. The ratio of the radii of the first Bohr orbit of He^+ ion to that of hydrogen is​

Answer 1

Answer :

r1(H^+) / r1(H) = 1/2

Step-by-step Explanation :

Given : Helium : atomic number (Z) = 2

mass number (A) = 4

To find : Ratio of the radii of the first Bohr orbit of He^+ ion to that of

hydrogen = ?

We know that ,

Radius of nth Bohr's orbit = n²h² / 4π²mZe²

Where,

n = Energy level,

h = planks constant,

m = mass,

Z = atomic number

e = charge

So for Hydrogen atom

Z = 1 and n = 1

r1 (H) = h²/ 4π²me² --------------(1)

So for He^+ ion,

Z = 2 and n = 1

r1 = h²/ 2 × 4π²me²

r1 ( H^+) = 1/2 × h²/4π²me² -------------(2)

Substituting h²/4π²me² = r1 (H) in equation (2)

We get,

r1 (H^+) = 1/2 × r1(H)

Therefore r1(H^+) / r1(H) = 1/2