Enter the mass number into the calculator to determine the nuclear radius of an atom. The nuclear radius is calculated using the empirical formula derived from the liquid drop model of the nucleus.
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Nuclear Radius Formula
The following formula is used to calculate the nuclear radius:
R = r₀ * A^{(1/3)}Variables:
- R is the nuclear radius (femtometers, fm)
- r₀ is the radius constant (approximately 1.2 fm)
- A is the mass number (number of protons and neutrons in the nucleus)
To calculate the nuclear radius, multiply the radius constant by the cube root of the mass number.
What is a Nuclear Radius?
The nuclear radius is the approximate radius of an atomic nucleus. It can be estimated using an empirical formula that relates the radius to the mass number of the nucleus. The formula assumes that the nucleus can be approximated as a sphere and that the volume of the nucleus is proportional to the number of nucleons (protons and neutrons) it contains. This concept is important in nuclear physics and helps in understanding the structure and stability of atoms.
How to Calculate Nuclear Radius?
The following steps outline how to calculate the Nuclear Radius.
- First, determine the mass number (A) of the nucleus.
- Next, use the radius constant (r₀), which is approximately 1.2 fm.
- Next, gather the formula from above = R = r₀ * A^(1/3).
- Finally, calculate the Nuclear Radius (R) in femtometers (fm).
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem:
Use the following variables as an example problem to test your knowledge.
Mass number (A) = 238
Using the formula R = r₀ * A^(1/3), where r₀ = 1.2 fm:
R = 1.2 * 238^(1/3) ≈ 7.44 fm
