Question

The half-life of krypton is 10.756 y. Calculate the number of disintegrations per second
of 2.25 g of krypton.​

Answer 1

Answer:

ANSWER

t

1/2

=1.42×10

17

s

1 gm of U contains =

235

6×10

23

=25.3×10

20

atoms

The decay rate:

R=λN

=

t

1/2

ln 2

×25.3×10

20

=

1.42×10

17

.693

×25.3×10

20

=0.1235×10

5

s

−1

Answer 2

Given:

Half-life of Krypton, t = 10.756 years

Mass in grams of krypton, m = 2.25 g

Find:

The number of disintegrations per second.

Solution:

The molar mass of krypton, M = 84 g/mol

Avogadro's number, Nₐ = 6.022 × 10²³

Number of atoms present in 2.25 g of krypton, N = (m/M)×Nₐ

                                                           N = (2.25 × 6.022 × 10²³)/84

                                                           N = 0.1613 × 10²³ atoms

Decay constant or disintegration constant, λ = 0.693/t

                                                                           = 0.693/10.756

                                                              = 0.0644 y⁻¹ = 0.0644/3600 s⁻¹

                                                              = 1.789 × 10⁻⁵ s⁻¹

∴ Number of disintegrations per second, r = λN

                                                            r = (0.1613 × 10²³) × (1.789 × 10⁻⁵)

                                                            r = 0.289 × 10²³⁻⁵ atoms/second

                                                            r = 0.289 × 10¹⁸ atoms/second

Hence, the number of disintegrations per second of 2.25 g of krypton is 0.289 × 10¹⁸ atoms/second.

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