A hydrogen atom is 5.3 × 10−10 m in radius. Use the uncertainty principle to estimate the minimum energy an electron can have in this atom.
Answer
According to uncertainty
P=ℏr=2.11∗10−20kg−m/sP=\frac{\hbar}{r}\\=2.11*10^{-20}kg-m/sP=rℏ=2.11∗10−20kg−m/s
So minimum energy
E=p2c2+m2c4E=\sqrt{p^2c^2+m^2c^4}E=p2c2+m2c4
Putting all values
E=3.3∗10−12J3.3*10^{-12}J3.3∗10−12J
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