Calculate the λSWL for molybdenum, when the accelerating potential is 15 kV
To calculate the λSWL (wavelength of the incident electrons) for molybdenum with an accelerating potential of 15 kV, we can use the equation:
λSWL = h / √(2 * m * e * V)
Where:
λSWL is the wavelength of the incident electrons
h is the Planck's constant (6.62607015 × 10⁻³⁴ J·s)
m is the mass of an electron (9.10938356 × 10⁻³¹ kg)
e is the charge of an electron (1.602176634 × 10⁻¹⁹ C)
V is the accelerating potential (15 kV)
Now, let's plug in the values and calculate:
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C) * (15 × 10³ V))
Simplifying the equation further:
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C) * (15 × 10³ V))
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C) * (15000 V))
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C) * (15000 V))
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C * 15000 V))
Now, plug in the values and calculate:
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (1.602176634 × 10⁻¹⁹ C * 15000 V))
Calculating further:
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (2.403264951 × 10⁻¹⁴ J))
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(2 * (9.10938356 × 10⁻³¹ kg) * (2.403264951 × 10⁻¹⁴ J))
Simplifying and calculating further:
λSWL = (6.62607015 × 10⁻³⁴ J·s) / √(4.380388455 × 10⁻⁴⁴ J²·s²)
λSWL = (6.62607015 × 10⁻³⁴ J·s) / (6.609881051 × 10⁻²² J·s)
λSWL = 10⁻¹² m
λSWL = 0.000000000001 meters
Therefore, the wavelength of the incident electrons for molybdenum with an accelerating potential of 15 kV is approximately 0.000000000001 meters (or 1 picometer).