An alpha particle, ^4 He^2+,
has a mass of 4.00151 amu. Find the value of its charge-to-mass ratio in C/kg.
charge = 2*1.602E-19 C
mass: convert amu to kg
Calculate C/kg
To find the charge-to-mass ratio of an alpha particle (^4He^2+), we need to determine its charge and mass individually, and then divide the charge by the mass.
The charge of an alpha particle is 2e, where "e" represents the elementary charge value which is 1.6 × 10^-19 C.
The mass of an alpha particle (^4He^2+) is given as 4.00151 amu.
To convert this mass to kilograms, we need to utilize the atomic mass unit (amu) conversion factor: 1 amu = 1.66054 × 10^-27 kg.
So, the mass of the alpha particle in kilograms is:
4.00151 amu × (1.66054 × 10^-27 kg/1 amu) = 6.644657 × 10^-27 kg.
Now we can calculate the charge-to-mass ratio by dividing the charge (2e) by the mass (6.644657 × 10^-27 kg):
(2e) / (6.644657 × 10^-27 kg) = [2 × (1.6 × 10^-19 C)] / (6.644657 × 10^-27 kg) ≈ 4.788 × 10^7 C/kg.
Therefore, the value of the charge-to-mass ratio for an alpha particle (^4He^2+) is approximately 4.788 × 10^7 C/kg.
To find the value of the charge-to-mass ratio for an alpha particle, we can use the formula:
charge-to-mass ratio = (charge of the particle) / (mass of the particle)
In this case, the charge of an alpha particle is equal to 2 times the elementary charge, which is approximately 1.602 x 10^-19 C.
Now, we need to convert the atomic mass unit (amu) to kilograms (kg). The atomic mass unit is defined as one-twelfth the mass of a carbon-12 atom, which is approximately 1.661 x 10^-27 kg.
So, let's calculate the charge-to-mass ratio:
charge-to-mass ratio = (2 * 1.602 x 10^-19 C) / (4.00151 amu * 1.661 x 10^-27 kg/amu)
Now, we can simplify this expression:
charge-to-mass ratio = 3.204 x 10^7 C/kg
Therefore, the charge-to-mass ratio of an alpha particle is approximately 3.204 x 10^7 C/kg.