Calculate number of protons and neutrons in Nitrogen isotopes 13N, 14N, 15N, 16N, and 17N

Question: Nitrogen (Atomic Number 7) has stable isotopes (half-life greater than 1 sec) of mass numbers 13, 14, 15, 16 and 17.  Calculate number of protons and neutrons in each of the isotopes of nitrogen.

Solution:

The Atomic Number (Z) of Nitrogen is 7. The atomic number is always equal to the number of protons. And the number of protons always equals the electron number in an uncharged atom so that the atom is electrically neutral.

Therefore, an uncharged Nitrogen atom always has 7 protons and 7 electrons.

 An isotope is formed when the neutron number varies in an atom of the same element. This changes the mass number in an atom’s nucleus since the mass number A is the sum of protons and neutrons. The proton number remains unchanged.

 mass number A= Number of protons (p) + number of neutrons (n)

 The mass number is written as a superscript next to the element’s symbol as,

So, the number of neutrons in different Nitrogen isotopes ¹³N, ¹⁴N, ¹⁵N, ¹⁶N, and ¹⁷N is-

¹³N Isotope:

Mass number =13 (Given)  

mass number (A) = number of protons (p) + number of neutrons (n)

A= p+ n

Therefore, n= A-p = 13-7 = 6.

Solution using log table-

n= A-p

Applying log₁₀ on both sides

log₁₀ n= log (A-Z)

log₁₀ n= log₁₀ (13-7) =log₁₀ 6=0.7782

Applying antilog,

n =Antilog (0.7782)

6.001 = 6

The number of neutrons in the ¹³N Isotope is 6, and the number of protons is 7.

¹⁴N Isotope

Mass number =14 (Given)  

mass number (A) = number of protons (p) + number of neutrons (n)

A= p+ n

Therefore, n= A-p = 14-7 = 7.

Solution using log table-

n= A-p

Applying log₁₀ on both sides

log₁₀ n= log (A-Z)

log₁₀ n= log₁₀ (14-7) = log₁₀ 7 =0.8451

Applying antilog,

n =Antilog (0.8451) = 7

The number of neutrons in the ¹⁴N Isotope is 7, and the number of protons is 7.

¹⁵N Isotope

Mass number =15 (Given)  

mass number (A) = number of protons (p) + number of neutrons (n)

A= p+ n

Therefore, n= A-p = 15 - 7 = 8.

Solution using log table-

n= A-p

Applying log₁₀ on both sides

log₁₀ n= log (A-Z)

log₁₀ n= log₁₀ (14-7) = log₁₀ 8 =0.9031

Applying antilog,

n =Antilog (0.9031) = 8

The number of neutrons in the ¹⁵N Isotope is 8, and the number of protons is 7.

¹⁶N Isotope

Mass number =16 (Given)  

mass number (A) = number of protons (p) + number of neutrons (n)

A= p+ n

Therefore, n= A-p = 16 - 7 = 9.

Solution using log table-

n= A-p

Applying log₁₀ on both sides

log₁₀ n= log (A-Z)

log₁₀ n= log₁₀ (16-7) = log₁₀ 9 =0.9542

Applying antilog,

n =Antilog (0.9542) = 9

The number of neutrons in the ¹⁶N Isotope is 9, and the number of protons is 7.

¹⁷N Isotope

Mass number =17 (Given)  

mass number (A) = number of protons (p) + number of neutrons (n)

A= p+ n

Therefore, n= A-p = 17 - 7 = 10.

Solution using log table-

n= A-p

Applying log₁₀ on both sides

log₁₀ n= log (A-Z)

log₁₀ n= log₁₀ (17-7) = log₁₀ 10 =1.000

Applying antilog,

n =Antilog (1.000) = 10

The number of neutrons in the ¹⁷N Isotope is 10, and the number of protons is 7.