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de Broglie proposed dual nature for elec...

de Broglie proposed dual nature for electron by putting his famous equation `lambda=h/(mv)`. Later on Heisenberg proposed uncertainity principle as `Deltap. Deltax ge h/(4pi)`. On the contrary, particle nature of electron was established on the basis of photoelectric effect. When a photon strikes the metal surface, it gives up its energy to the electron. Part of this energy (say W) is used by the electrons to escape from the metal and the remaining energy imaprts kinetic energy `(1//2 mv^(2))` to the ejected photoelectron. The potential applied on the surface to reduce the velocity of photoelectron to zerp is known as stopping potential.
The circumference of thired orbit of a single electron species is `3 nm`. What may be the approximate wavelength of the photon required to just ionize electron from this orbit.

A

`19.2xx10^(-2) m`

B

`5.76xx10^(-2) m`

C

`3.84xx10^(-2) m`

D

`1.92xx10^(-2) m`

Text Solution

Verified by Experts

The correct Answer is:
D
`Deltax=(h)/(4pi Me)xx1/(DeltaV)" "DeltaV=V 0.001/100=300xx10^(-5) m//s`
`Deltax=5.8xx10^(-5)xx1/(300xx10^(-5))=1.92xx10^(-2) m`
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de Broglie proposed dual nature for electron by putting his famous equation lambda = (h)/(mv). Later on, Heisenberg proposed uncertainty principle as deltapDeltax ge (h)/(4pi). On the contrary, Particle nature of electron was established on the basis of photoelectric effect. When a photon strikes the metal surface it gives up its energy to the electron. Part of this energy (say W) is used by the electrons to escape from the metal and the remaining energy imparts kinetic energy (1//2 mv^(2)) to the ejected photoelectron. The potential applied on the surface to reduce the velocity of photoelectron to zero is known as stopping potential . The circumference of third orbit of a single electron species is 3 nm. What may be the approximate wavelength of the photon required to just ionize electron from this orbit?

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