Name: Theories of Nuclear Stability
Uploaded: 2019-07-19
Duration: 4 min 23 s
Description: Nuclear stability means that the nucleus of an element is stable and thus, it does not decay spontaneously, emitting any kind of radioactivity. What makes it...

Question

If the average life time of an excited state of

H

atom is of order

10^{- 8} \sec

, estimate how many orbits an

e^{- 7}

makes when it is in the state

n = 2

and before it suffers a transition to

n = 1

state.

Accepted Answer

Velocity of an electron in $n^{th}$ orbit is given by,

$v_{n} = 2.18 \times 10^{6} \frac{Z}{n} m / s$

Velocity of electron in $n = 2$ ,

$v_{2} = 2.18 \times 10^{6} \times \frac{1}{2} m / s v_{2} = 1.09 \times 10^{6} m / s$

We know, distance $=$ speed $\times$ time

So, distance travelled by electron $= 1.09 \times 10^{6} \times 10^{- 8} m = 1.09 \times 10^{- 2} m$

Circumference of orbit $= 2 πr = 2 π \times 0.529 \times \frac{n^{2}}{Z} \overset{\circ}{A} = 2 \times 3.14 \times 0.529 \times 2^{2} \times 10^{- 10} = 13.28 \times 10^{- 10} m$

Hence, number of revolutions made by the electron $= \frac{1.09 \times 10^{- 2}}{13.28 \times 10^{- 10}} = 8.2 \times 10^{6}$

If the average life time of an excited state of $H$ atom is of order $10^{- 8} \sec$ , estimate how many orbits an $e^{- 7}$ makes when it is in the state $n = 2$ and before it suffers a transition to $n = 1$ state.

Important Questions on Structure of Atom

Learn and Prepare for any exam you want !

If the average life time of an excited state of H atom is of order 10-8sec, estimate how many orbits an e-7 makes when it is in the state n=2 and before it suffers a transition to n=1 state.

Important Questions on Structure of Atom

Learn and Prepare for any exam you want !

If the average life time of an excited state of $H$ atom is of order $10^{- 8} \sec$ , estimate how many orbits an $e^{- 7}$ makes when it is in the state $n = 2$ and before it suffers a transition to $n = 1$ state.