Carbon-14 is a radioactive isotope which decays with a half-life of 5730 years. what is the first-order rate constant for its decay, in units of years–1?

In chemical equilibrium, radioactive decay occurs because of unstability due to the high neutron-to-proton ratio. Through time, the radioactive element is converted to a new element. This radioactive decay undergoes first order reaction. Its equation is in the form of 

A = A₀e^(-kt), where A is the amount of the element after time t, A₀ is the original amount of element at t=0 and k is the rate constant. 

Half-life is the amount of time for A to be 1/2 of A₀. Modifying the equation during half time, we let A=1/2 A₀. Then.

1/2 A₀ = A₀e^(-kt)
1/2 = e^(-k(5730))
k = 0.000121

Thus, the first-order rate constant is equal to 0.000121 per year.

assuming that your periodic table has eighteen columns, you should highlight   the four elements in the third column from the left of the table.

explanation

neutral atoms of elements after calcium contain d electrons. the energy of d orbitals of a particular main shell lies between the energy of the s and p orbitals of the next main shell. for example, electrons in the have energy higher than those in the orbital while lower than those of the orbital.

by the aufbau principle, electrons fill orbitals one at a time, starting from those of the lowest energy. the orbital is therefore filled right after orbitals and before orbitals.  

potassium has electron configuration and calcium . the s orbital of a main shell holds a maximum of two electrons. the next element would thus have the electron configuration and satisfy the requirements.

a neutral atom of the element contains three electrons on top of the most recent noble gas element. it should thus be placed in the third column of the periodic table. both scandium and yttrium would satisfy the conditions. an aufbau diagram indicates that the 4f orbital is filled before the 5d. however, it appears that exceptions exists for both lanthanum and actinium. neutral atoms of the two d-block elements also demonstrate the and should be highlighted as well.

Ibelieve the answer is d