As the atomic radius decreases, electrons are drawn closer to the nucleus. Since the electromagnetic force between the positively charged nucleus and negatively charged electrons is a function of distance, the force of attraction, or effective nuclear charge, exerted on each electron will be greater.

To write out the shorthand electronic configuration for Ga, you simply write down the noble gas that that comes before , in this case , then write the rest of the electron configuration as normal.

E=hf, or E=hc/λ

h is Planck's constant with a value of 6.62606957 × 10^-34 m² kg / s. Converting 475nm to m gives 4.75x10^-7m. c is the speed of light with 3x10⁸m/s. Putting these variables into the second equation you get 4.174x10^-19J

The atomic number is equal to the number of protons, because no two elements have the same number of protons. It is however possible for different elements to have the same number of electrons (through the loss or gain of electrons) or neutrons (isotopes). 

This is the definition of gamma radiation.

During alpha decay, an element emits a helium nucleus with 2 neutrons and 2 protons. Thus, the atomic mass of the new element is decreased by four, and the atomic number is decreased by two.

Three subsequent alpha decays result in a new element with an atomic mass of 232 - 3(4) = 220, and a new atomic number of 90 - 3(2) = 84.

Using the periodic table, we find the element with this atomic number is polonium (Po).

In alpha decay, a helium nucleus is emitted, and thus the isotope loses 2 protons and 2 neutrons.

In electron emission, a neutron in the nucleus is converted into a proton and an emitted electron.

In positron emission, a proton in the nucleus is converted into a neutron and an emitted positron.

The given isotope will lose 4 protons and 4 neutrons via alpha emission, gain 1 proton and lose 1 neutron via electron emission, and lose 2 protons and gain 2 neutrons via positron emission. The result is a loss of 5 protons and 8 mass units.

Accounting for the changes in atomic mass and number, we find that the final element is 141-praseodymium.

In alpha decay, an element loses the equivalent of a helium nucleus, or 2 protons and 2 neutrons. Uranium-238 has an atomic number of 92 and a mass of 238 units, so the product of alpha decay will have an atomic number of 90 and a mass of 234 units. This corresponds to thorium-234.

With each half-life, the amount of Am-242 is halved. 4 days is 96 hours, which is 6 half-lives. For half-life questions use the formula:

Where  is the number of half lives. 

Thus  of Am-242 is left after 4 days.

An alpha particle can be written as  or . The latter is used frequently in nuclear physics because it is more helpful when calculating resulting nuclei after radioactive decay. In alpha emission, the nucleus loses two protons and two neutrons.