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

Answer 1

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