What is the radius of a real or imaginary nucleus of 46X100
do I use the formula
R = R_o * A^(1/3)
and therefore
(1.3*10^-15)* 100^(1/3)
=6.0340655e-15?
To calculate the radius of a nucleus, you can indeed use the formula you mentioned:
R = R_o * A^(1/3)
Where R is the radius of the nucleus, R_o is a constant (approximately 1.3 × 10^-15 m), and A is the mass number of the nucleus.
In your case, you have a nucleus with a mass number of A = 100. So, plugging these values into the formula, we have:
R = (1.3 × 10^-15) * 100^(1/3)
Let's evaluate this expression:
First, calculate 100 raised to the power of 1/3:
100^(1/3) ≈ 4.6416
Now substitute this value back into the formula:
R ≈ (1.3 × 10^-15) * 4.6416
Finally, calculate the numerical value:
R ≈ 6.039 × 10^-15 meters
Therefore, the radius of the nucleus is approximately 6.039 × 10^-15 meters. Please note that the value you obtained (6.0340655 × 10^-15 meters) differs slightly due to rounding errors in the intermediate steps.