calculate the uncertainty in the position of a hydrogen atom when its velocity is known to be within 50.0 m/s. How does the uncertainty in position compare to the radius of the hydrogen atom at approximately 0.040 nm (1 amu = 1.66 * 10^-27 kg).  really struggling on the second part of the question. thank you.

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Asked Sep 22, 2019
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calculate the uncertainty in the position of a hydrogen atom when its velocity is known to be within 50.0 m/s. How does the uncertainty in position compare to the radius of the hydrogen atom at approximately 0.040 nm (1 amu = 1.66 * 10^-27 kg). 

 

really struggling on the second part of the question. thank you. 

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Expert Answer

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Step 1

It is given that:

Uncertainty in velocity = 50.0 m/s

Mass of hydrogen atom = 1.66×10-27 kg

Radius of hydrogen atom = 0.040 nm

Step 2

Heisenberg uncertainty principle states that it is impossible to determine the exact position and velocity of a particle simultaneously. The mathematical expression for Heisenberg uncertainty principle is given as follows:

h
Дх. Др 2
4Tt
where, Ax is uncertainty in position
Ap is uncertainty in momentum (Ap = mAv)
h is planck's constant (h=6.626x1034 J.s
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h Дх. Др 2 4Tt where, Ax is uncertainty in position Ap is uncertainty in momentum (Ap = mAv) h is planck's constant (h=6.626x1034 J.s

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Step 3

Thus, the uncertainty in position of hydroge...

h
Ax.mAv
4Tt
Ax =
4πην
6.626x1034 J.S
4x3.14x1.66x102 kgx50.0 ms1
6.626x1034 kg.m2.s2.s
4x3.14x1.66x102 kgx50.0 ms1
Since, 1 J1kg.m2.s2
6.626x 1034-27 m
1042.48
= 0.0063x107 m
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h Ax.mAv 4Tt Ax = 4πην 6.626x1034 J.S 4x3.14x1.66x102 kgx50.0 ms1 6.626x1034 kg.m2.s2.s 4x3.14x1.66x102 kgx50.0 ms1 Since, 1 J1kg.m2.s2 6.626x 1034-27 m 1042.48 = 0.0063x107 m

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