A beam of electrons is accelerated from rest and then passes through a pair of identical thin slits that are 1.35 nm apart. You observe that the first double-slit interference dark fringe occurs at ±15.0 ∘ from the original direction of the beam when viewed on a distant screen. Through what potential difference were the electrons accelerated?

The potential difference was 3.09V.

Explanation:

The condition for the first dark fringe is

.

putting in numbers we get:

Now, from de broglie relation we know that

or

where  is Planck's constant and is electron momentum. The momentum is related to kinetic energy by

this energy we know must come from potential difference; therefore,

substituting the value of from equation (2), and solving for potential , we get:

putting in numerical values in equation (4) we get:

.

Therefore, the potential difference through which the protons were accelerated was 3.09V.

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