Question:
Which of the following is the correct unit of angular momentum of an electron in an orbital of an atom?
Which of the following is the correct unit of angular momentum of an electron in an orbital of an atom?
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Planck's constant ($h$) has units of "action," which is Energy $\times$ Time (J s). Since angular momentum is expressed in units of $h$, its unit is J s.
Updated On: May 1, 2026
- J s
- J s
- W s$^2$
- W s
- J s$^2$
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The Correct Option is A
Solution and Explanation
Concept:
Angular momentum ($L$) for an electron in an atom is quantized and given by Bohr's second postulate as $L = \frac{nh}{2\pi}$. The units of angular momentum are the same as the units of Planck's constant ($h$).
Step 1: {Analyze the formula for angular momentum.}
Angular momentum is defined as $L = mvr$.
• Mass ($m$) is in $kg$
• Velocity ($v$) is in $m/s$
• Radius ($r$) is in $m$ Units of $L = kg \cdot m^2 / s$.
Step 2: {Relate Joules to the base units.}
Energy (Joule) is work done, $J = N \cdot m = (kg \cdot m / s^2) \cdot m = kg \cdot m^2 / s^2$.
Step 3: {Match units.}
Multiply $J$ by $s$: $$J \cdot s = (kg \cdot m^2 / s^2) \cdot s = kg \cdot m^2 / s$$ This matches the units of angular momentum.
Step 1: {Analyze the formula for angular momentum.}
Angular momentum is defined as $L = mvr$.
• Mass ($m$) is in $kg$
• Velocity ($v$) is in $m/s$
• Radius ($r$) is in $m$ Units of $L = kg \cdot m^2 / s$.
Step 2: {Relate Joules to the base units.}
Energy (Joule) is work done, $J = N \cdot m = (kg \cdot m / s^2) \cdot m = kg \cdot m^2 / s^2$.
Step 3: {Match units.}
Multiply $J$ by $s$: $$J \cdot s = (kg \cdot m^2 / s^2) \cdot s = kg \cdot m^2 / s$$ This matches the units of angular momentum.
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