Question

According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to ______.

Options

• `"Z"^2/"n"^2`

• `"Z"/"n"`

• `"n"/"Z"`

• `"n"^2/"Z"`

Answer 1

According to Bohr's theory, the radius of the nth Bohr orbit of a hydrogen like atom of atomic number Z is proportional to `underlinebb("n"^2/"Z")`.

Explanation:

According to Bohr's theory, the coulomb force on the electron causes its centripetal acceleration.

⇒ `1/(4piepsilon_0)"Ze"^2/"r"^2="mv"^2/"r"`

Also one of Bohr's postulates states mvr = `"nh"/(2pi)`

Thus eliminating v from the equations gives

⇒ r ∝ `"n"^2/"Z"`