## What are nuclear magic numbers?

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons, separately) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126 (sequence A018226 in the OEIS).

### How do you find the magic number in nuclear physics?

The conventional magic numbers are {2, 8, 20, 28, 50, 82, 126}. These numbers were found in the case of protons by comparing the number of stable isotopes for different proton numbers. For neutrons the magic numbers were found by comparing the number of stable nuclides with the same neutron numbers.

#### What are the magic numbers for both proton and neutron?

The double numbers only occur for isotopes that are heavier, because the repulsion of the forces between the protons. The magic numbers are: proton: 2, 8, 20, 28, 50, 82, 114. neutron: 2, 8, 20, 28, 50, 82, 126, 184….Magic Numbers.

Proton number (Z) | Neutron Number | # of stable Isotopes |
---|---|---|

Odd | Even | 50 |

Odd | Odd | 4 |

**How do you calculate nuclear stability?**

The two main factors that determine nuclear stability are the neutron/proton ratio and the total number of nucleons in the nucleus. The principal factor for determining whether a nucleus is stable is the neutron to proton ratio.

**Is 8 a magic number?**

The numbers 8, 20 and 28 are magic numbers. The number 28 could not be a special number for a subshell because it is the number for a fully filled shell.

## Is 6 a magic number?

The examination of the incremental binding energies reveals the magicality of the conventional nuclear magic numbers, but it also reveals that 6 and 14 are magic numbers. It is a very remarkable fact the filled shell numbers are the same for protons as for neutrons.

### What is a balanced nuclear equation?

A balanced nuclear equation is one where the sum of the mass numbers (the top number in notation) and the sum of the atomic numbers balance on either side of an equation. Nuclear equation problems will often be given such that one particle is missing.

#### Is six a magic number?

Six is the magic number because it divides into pairs, and into the original magic number of three.

**How to translate the number of States to the nuclear magic numbers?**

Translation of the Number of States to the Nuclear Magic Numbers Shell Number Number of States (not counting spin) Number of States (counting spin) Cumulative Sum 1 1 2 2 2 2 4 6 3 4 8 14 4 7 14 28

**What are the magic numbers of a nucleus?**

One of the elements of the physics of nuclei is the matter of magic numbers. They represent a shell being completely filled so additional nucleons have to go into a higher shell. A higher shell involves a greater separation from the other nucleons and lower interaction energy. The conventional magic numbers are {2, 8, 20, 28, 50, 82, 126}.

## Are there any magic numbers for protons or neutrons?

The seven most widely recognized magic numbers as of 2019 are 2, 8, 20, 28, 50, 82, and 126 (sequence A018226 in the OEIS). For protons, this corresponds to the elements helium, oxygen, calcium, nickel, tin, lead and the hypothetical unbihexium, although 126 is so far only known to be a magic number for neutrons.

### How are magic numbers related to shell capacities?

If only the conventional magic numbers {2, 8, 20, 28, 50, 82, 126} are considered the shell capacities are {2, 6, 12, 8, 22, 32, 44}. Thus there is the anomaly of the shell capacity decreasing from 12 to 8 rather than increasing for each higher shell number as occurs for all of the other cases.