The ratio between total acceleration of the electron in singly ionized helium atom and hydrogen atom (both in ground state) is

Options

A. 2
B. 4
C. 8
D. 16

Answer

C

Explanation

Acceleration of the electron a `=(v^2)/(r )`
But `v prop Z/n " and " r prop n^2/Z`
`therefore a prop Z^2/n^2 xxZ/n^2 i.e. a prop Z^3/n^4`
But both of them are in the ground state or n=1
`therefore a prop Z^3 therefore (""^aHe^+)/(""^aH) = ((Z_(He^+))/(Z_H))^3 = (2/1)^3 = 8`