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Answer :
None of the given options A, B, C, D, or E accurately represent the magnitude of the electron spin angular momentum. The correct magnitude is approximately 9.612 × 10⁻³⁵ J·s.
The magnitude of the electron spin angular momentum is determined by the formula:
Magnitude = √(s(s+1)ħ²)
Where:
- s represents the spin quantum number of the electron, which is equal to 1/2 for electrons.
- ħ is the reduced Planck's constant, which is approximately equal to 1.054 × 10⁻³⁴ J·s.
Substituting the values, we have:
Magnitude = √((1/2)((1/2)+1)(1.054 × 10⁻³⁴ J·s)²)
Simplifying the equation:
Magnitude = √((1/2)(3/2)(1.054 × 10⁻³⁴ J·s)²)
Magnitude = √(3/4)(1.054 × 10⁻³⁴ J·s)²)
Magnitude = √(3/4)(1.054 × 10⁻⁶⁸ J²·s²)
Magnitude = √(3/4)(1.109 × 10⁻⁶⁸ J²·s²)
Magnitude = √(3/4)(1.109 × 10⁻⁶⁸J²·s²)
Magnitude = √(3/4) × 1.109 × 10⁻³⁴J·s
Magnitude = √(3/4) × 1.109 × 10⁻³⁴ J·s
Magnitude = √(3/4) × 1.109 × 10⁻³⁴ J·s
Magnitude = (0.866) × 1.109 × 10⁻³⁴ J·s
Magnitude ≈ 9.612 × 10⁻³⁵ J·s
Therefore, none of the given options A, B, C, D, or E accurately represent the magnitude of the electron spin angular momentum. The correct magnitude is approximately 9.612 × 10⁻³⁵ J·s.
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None of the provided answer options accurately represent the magnitude of electron spin angular momentum.
The magnitude of the electron spin angular momentum is not provided in the answer options you have listed. The options given are in units of nm−eV/c, which does not represent the magnitude of electron spin angular momentum. The magnitude of electron spin angular momentum is given by the formula:
L = √(s(s+1)ħ²)
where s is the spin quantum number (which is 1/2 for electrons) and ħ is the reduced Planck's constant. Using this formula, we can calculate the magnitude of electron spin angular momentum. Plugging in the values, we get:
L = √(1/2(1/2+1)ħ²)
L = √(3/4ħ²)
L = √(3/4)ħ
So, the magnitude of electron spin angular momentum is √(3/4) times the reduced Planck's constant, ħ. Therefore, none of the provided answer options accurately represent the magnitude of electron spin angular momentum.
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