1. Calculate the radius of orbit for a hydrogen electron in the n=3 level.

2.The half life of an unknown substance is one minutes. If the initial number of particles is 20 how many particles will remain after two minutes have elapsed?

1. To calculate the radius of orbit for a hydrogen electron in the n=3 level, we can use the formula for the Bohr radius. The Bohr radius (a₀) is given by:

a₀ = (0.529 * n²) / Z,

where n is the principal quantum number and Z is the atomic number.

For hydrogen, Z = 1. Substituting n = 3 and Z = 1 into the formula, we have:

a₀ = (0.529 * 3²) / 1 = 4.75 angstroms.

Therefore, the radius of the electron's orbit in the n=3 level of hydrogen is 4.75 angstroms.

2. To calculate the number of particles remaining after a certain time has elapsed, we can use the formula for exponential decay. The formula is:

N = N₀ * (1/2)^(t / t₁/₂),

where N is the final number of particles, N₀ is the initial number of particles, t is the elapsed time, and t₁/₂ is the half-life of the substance.

In this case, the half-life is given as one minute, so t₁/₂ = 1 minute. We want to calculate the number of particles remaining after two minutes, so t = 2 minutes.

Substituting N₀ = 20, t = 2, and t₁/₂ = 1 into the formula, we have:

N = 20 * (1/2)^(2 / 1) = 20 * (1/2)^2 = 20 * (1/4) = 5.

Therefore, after two minutes have elapsed, there will be 5 particles remaining.