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Question
The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly ______.
Options
1.2 nm
1.2 × 10–3 nm
1.2 × 10–6 nm
1.2 × 101 nm
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Solution
The wavelength of a photon needed to remove a proton from a nucleus which is bound to the nucleus with 1 MeV energy is nearly `underline(1.2 xx 10^-3 nm)`.
Explanation:
According to Einstein’s quantum theory light propagates in the bundles (packets or quanta) of energy, each bundle is called a photon and possessing energy. Energy of photon is given by
`E = hv = (hc)/λ`; where c = Speed of light, h = Planck's constant = `6.6 xx 10^-34` J-sec, v = Frequency in Hz, λ = the minimum wavelength of the photon required to eject the proton from nucleus.
In electron volt, `E(eV) = (hc)/(eλ) = 12375/(λ(Å)) = 12400/(λ(Å))`
According to the problem,
Energy of a photon, E = 1 MeV or 106 eV
Now, hc = 1240 eV nm
Now, `E = (hc)/λ`
⇒ λ = `(hc)/E = 1240/10^6` nm
= 1.24 × 10–3 nm
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