Name: De Broglie's Explanation of Bohr's Second Postulate
Uploaded: 2019-07-19
Duration: 1 min 30 s
Description: How does one explain Bohr's second postulate of quantisation of orbital angular momentum using de Broglie's hypothesis? Watch this video and find out.

Question

Determine the radius of the first orbit of the hydrogen atom. What would be the velocity and frequency of the electron in the first orbit?

Given: $h = 6.62 \times 10^{- 34} Js, m = 9.1 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}$

Accepted Answer

We know that the radius of an orbit in hydrogen atom is given by:

$r = \frac{n^{2} h^{2}}{4 π^{2} m K e^{2}}$

Given: $h = 6.62 \times 10^{- 34} Js, m = 9.1 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}, n = 1$

Putting all these values in the formula, we get,

$r = \frac{(1^{2}) {(6.6 \times 10^{- 34})}^{2}}{4 \times {(3.14)}^{2} \times (9.1 \times 10^{- 31}) \times 9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}} r = 5.3 \times 10^{- 11} m - - - (i)$

The velocity of electron in Bohr's orbit for hydrogen atom is given by:

$v = \frac{2 π K e^{2}}{n h}$

Given: $h = 6.62 \times 10^{- 34} Js, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}, n = 1$

Putting all these values in the formula, we get,

$v = \frac{2 \times 3.14 \times 9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{6.6 \times 10^{- 34}} v = 2.2 \times 10^{6} m / s$

The frequency of electron in Bohr's stationary orbit for a hydrogen atom is given by:

$ν = \frac{K e^{2}}{n h r}$

Given: $h = 6.62 \times 10^{- 34} Js, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}, n = 1$

Also, $r = 5.3 \times 10^{- 11} m$ from $(i)$

Putting all the values in the formula, we get,

$ν = \frac{9 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{1 \times 6.6 \times 10^{- 34} \times 5.3 \times 10^{- 11}} ν = 6.6 \times 10^{15} Hz$

Determine the radius of the first orbit of the hydrogen atom. What would be the velocity and frequency of the electron in the first orbit?

Given: $h = 6.62 \times 10^{- 34} Js, m = 9.1 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}$

Important Questions on Atoms

Learn and Prepare for any exam you want !

Determine the radius of the first orbit of the hydrogen atom. What would be the velocity and frequency of the electron in the first orbit? Given: h = 6.62×10-34 Js, m = 9.1×10-31 kg, e = 1.6×10-19 C, k = 9×109 Nm2C-2

Important Questions on Atoms

Learn and Prepare for any exam you want !

Determine the radius of the first orbit of the hydrogen atom. What would be the velocity and frequency of the electron in the first orbit?

Given: $h = 6.62 \times 10^{- 34} Js, m = 9.1 \times 10^{- 31} kg, e = 1.6 \times 10^{- 19} C, k = 9 \times 10^{9} {Nm}^{2} C^{- 2}$