Obtain approximately the ratio of the nuclear radii of the gold isotope 19779 Au and the silver isotope 10747 Ag .
The mass number of gold isotope A 79 197 u is 197 and the mass number of silver isotope A 47 107 g is 107 .
The radius of an isotope is directly proportional to its mass number.
R ∝ A 1 3
Where, R is the radius of the nucleus and A is the mass number.
The ratio of radii of two nuclei is given as,
R Au R Ag = ( A Au A Ag ) 1 3
By substituting the given values in above equation, we get
R Au R Ag = ( 197 107 ) 1 3 = 1.2256 ≈ 1.23
Thus, the ratio of nuclear radii of gold and silver isotopes is 1.23 .
The mass number of gold isotope
The radius of an isotope is directly proportional to its mass number.
Where,
The ratio of radii of two nuclei is given as,
By substituting the given values in above equation, we get
Thus, the ratio of nuclear radii of gold and silver isotopes is
