Practise Edexcel A-Level Physics de Broglie wavelength with particle momentum, speed comparisons and electron wave-behaviour evidence.
Niels Bohr developed an early model of the atom where electrons could only exist in fixed orbits around a nucleus. When an atom is ionised, an electron moves from its orbit around the nucleus to be free of the atom. Bohr derived an expression for the ionisation energy E, in joules, for a hydrogen atom:
(khe2)2×8m
where m is the mass of the electron, e is the charge of the electron, k=8.85×10−12CV−1m−1, and h is the Planck constant.
The Bohr model can also be used to predict an approximate radius for an atom. The equation for the radius r of the hydrogen atom is:
r=πme2h2k
where m is the mass of the electron.
A student suggests that, for a speed of 1.4×107ms−1, neutrons would have a wavelength similar to the radius of a hydrogen atom. Determine whether the student is correct.
mass of neutron =1.67×10−27kg
Substitutes values into r=πme2h2k
(1)
r=5.3×10−11( m)
(1)
Use of λ=h/p
(1)
λ=2.8×10−14( m) (for neutron)
(1)
neutron wavelength not similar to size of atom radius, so student is incorrect
(1)
(MP5 is dependent upon awarding all of MP1-4 and there needs to be some comparison of the two values)
(allow MP1 and/or MP3 for candidates who substitute the incorrect mass into the equation e.g. mass of neutron where it should be mass of electron in MP1)
r=5.31×10−11 m
For neutron, λ=h/p=(6.63×10−34Js)/(1.67×10−27 kg)(1.4×107 m s−1)=2.84×10−14 m