Question

An electron detector is 1.6 mm wide. What is the range of velocities it can detect?

Answer 1

E = mc²

E =
where L=wavelength of light
Hence,
mc² = .................(1)

Using formula for diffraction grating,

n = d * sin

n = 1, for first order diffraction

Maximum positive value of sin is 1

hence, maximum value of = d .................(2)
and minimum value of   = 0 ;
Now ,
Using formula (1),

when d = 1.6 mm , and sin = 1 ;

= 0.452 m/s
when sin = 0 ;

but maximum possible speed attainable is 3 * 10⁸  m/s.
Hence 0.452 < < 3 * 10⁸

Note: I have to tried to give the maximum possible theoretical answer neglecting a lot of factors like energy of excitation,type of detector etc, as they were not mentioned in the question. The answer is simply an indication of the approach that may be followed and may not be correct.