1 atomic mass unit is equal to 1.6605 × 10⁻²⁷Kg
Mass, m = 19.992 amu = 19.992 × 1.6605 × 10⁻²⁷
= 3.321 × 10⁻²⁶Kg
Speed, v = 2.0 × 10⁵ m/s
De Brogile equation:
Wavelength = h/mv
= 6.626 × 10³⁴ / (3.321 × 10⁻²⁶ × 2.0 × 10⁵)
= 9.976 × 10⁻¹⁴ m = 0.9976 × 10⁻¹³ m = 1.0 × 10⁻¹³ m
The wavelength associated with a [tex]20Ne^+[/tex] ion is equal to [tex]9.98 \times 10^{-14}[/tex] meters.
Given the following data:
To calculate the wavelength associated with a [tex]20Ne^+[/tex] ion, we would use De Broglie's equation:
First of all, we would determine the mass of a [tex]20Ne^+[/tex] ion.
1 atomic mass unit = [tex]1.6605 \times 10^{-27}\;Kg[/tex]
19.992 atomic mass unit = X Kg
Cross-multiplying, we have:
[tex]X = 19.992 \times 1.6605 \times 10^{-27}\\\\X = 3.32 \times 10^{-26}\; Kg[/tex]
Mathematically, De Broglie's equation is given by the formula:
Where:
W is the wavelength of a wave particle.
h is planck's constant (6.626 x 10⁻³⁴ J.s).
m is the mass of a wave particle.
v is the speed of a wave particle.
Substituting the given parameters into the formula, we have;
[tex]W = \frac{6.626 \times 10^{-34}}{3.32 \times 10^{-26} \times \;2.0 \times 10^5}\\\\W = \frac{6.626 \times 10^{-34}}{6.64 \times 10^{-21}}[/tex]
Wavelength = [tex]9.98 \times 10^{-14}[/tex] meters
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