AP EAPCET 04-Jul-2022 Shift 1 Paper

Given, ∆x= uncertainty in position
∆v= uncertainty in velocity
we know, ∆p=m∆v, where ∆p is the uncertainty in momentum and m is the mass of particle.
Using Heisenberg's uncertainty principle,
∆x⋅m∆v=‌

h

4π

As ∆x=∆v,
So, ∆v⋅m∆v=‌

h

4π

On multiplying both sides with m, we get
m∆v⋅m∆v=‌

mh

4π

Thus, ‌‌∆p2=‌

mh

4π

⇒∆p=√‌

mh

4π

.
Hence, ‌‌∆p=‌

1

2

√‌

mh

π