Question

Electromagnetic radiation is emitted when a neutron and proton fuse to make a deuteron. What is the wavelength of this radiation?

Answer 1

mass of proton = 1.6726 x 10^-27 kg

mass of neutron = 1.6749 x 10^-27 kg

mass of deuteron= 3.34 x 10^-27 kg

Missing mass = (1.6726 +1.6749 - 3.34) x 10^-27 kg = 0.0075 x 10^-27 kg

Energy released E = mc² , c is velocity of light = 3 x 10⁸ m/s

                              = 0.0075 x 10^-27 kg x (3 x 10⁸ m/s)²

                               = 6.75 x 10^-13 J

We know that E = hc/wave length   , h = planck’s constant = 6.626 x 10^-34 J.s

Then,
wave length = hc/E

                      = [6.626 x 10^-34 J.s x 3x 10⁸ m/s] /6.75 x 10^-13 J

                      = 2.94 x 10^-13 m

                  = 2.94 x 10^-4 x 10^-9 m

                      = 2.94 x 10^-4 nm                                 [ 1 nm = 10^-9 nm]

Therefore,

wave length of given radiation = 2.94 x 10^-4 nm