Question

If '`lambda_1`' and '`lambda_2`' are de-Broglie wavelengths for electrons in first and second Bohr orbits in hydrogen atom, then the ratio '`lambda_2`' to '`lambda_1`' is (E₁ = -13.6 eV) ____________.

Options

• 4 : 1

• 16 : 1

• 8 : 1

• 2 : 1

Answer 1

If '`lambda_1`' and '`lambda_2`' are de-Broglie wavelengths for electrons in first and second Bohr orbits in hydrogen atom, then the ratio '`lambda_2`' to '`lambda_1`' is 2 : 1.

Explanation:

`lambda_1 = "h"/("mV"_1), lambda_2 = "h"/("mV"_2)`

`therefore lambda_2/lambda_1 = "V"_1/"V"_2`

`"But V" prop 1/"n"`

`therefore "V"_1/"V"_2 = 2/1`

`therefore lambda_2/lambda_1 = 2/1`