ATOMS AND NUCLEI

Answer :

in t = 40 days, substance decays to (1 / 16) of original i.e. fraction left is

                   (1 / 16).

                   If half life is T_(1/2) then fraction left = (N / N₀) = (1 / 2)^{[t / {T(1/2)}]}

                                      ∴       (1 / 16)  = (1 / 2)^{[(40) / {T(1/2)}]}

                                      ∴        (1 / 2)⁴ = (1 / 2)^{[(40) / {T(1/2)}]}

                                      ∴              4 = [(40) / T_(1/2)]

                                      ∴       T_(1/2) = (40 / 4) = 10 days.

Answer :

For atom in any state, E_n = [(13.6) / n²] Z²

                   For lithium, Z = 3 & for second excited state, n = 3 hence

                             E_n = [{13.6 × (3)²} / (3)²] = 13.6 eV.    

Answer :

For the Balmer series, (1 / λ) = R[(1 / 2²) – (1 / n²)]

                   for maximum wavelength, (1 / λ_max) = R[(1 / 4) – (1 / 3²)] ----- n = 3

                                                          (1 / λ_max) = R[(9 – 4) / (36)]

                             ∴ λ_max = (36 / 5R)

                   for minimum wavelength n = ∞

                             ∴ (1 / λ_min) = R[(1 / 4) – (1 / ∞)]

                                (1 / λ_min) = (R / 4)

                             ∴       λ_min = (4 / R)

                             ∴ [(λ_max) / (λ_min)] = (36 / 5R) × (R / 4) = (36 / 20) = (9 / 5)

                             i.e. [(λ_min) / (λ_max)] = (5 / 9).  

Answer :

given T_(1/2) = 24000 yrs

                             t = 72000 yrs

                   we know fraction left = (N / N₀) = (1/2)^{[t / {T(1/2)}]}

                             hence (N / N₀) = (1 / 2)^{[(72000) / (24000)]} = (1 / 2)³

                                      ∴ (N / N₀) = (1 / 8). 

Answer :

if we observe A – Z = (14 – 7) = (13 – 6) = 7

                   i.e. A – Z is same i.e. number of neutrons are same.

                   Hence they are isotones.