Question

1 mole of an element emitting alpha particle in a vessel which store them . Half life of that element is 5 hr . How long would it take for 4.515×10^23 alpha particle to be stored in that vessel?

Answer 1

answer : 10 hrs

1 mole of alpha particles in given element = 6.023 × 10²³

half life of that element, T½ = 5 hrs

⇒ ln2/λ = 5 hrs

⇒λ = ln2/5

now using formula, t = 1/λ ln[a/(a - x)]

= 5/ln2 ln[6.023 × 10²³/(6.023 - 4.515) × 10²³ ]

= 5/ln2 ln(4/1)

= 5ln(4)/ln2

= 10 hrs

hence 10 hrs would take for 4.515 × 10²³ alpha particles to be stored in that vessel.

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Answer 2

$\huge\star\mathfrak\blue{{Answer:-}}$

1 mole of alpha particles in given element = 6.023 × 10²³

half life of that element, T½ = 5 hrs

⇒ ln2/λ = 5 hrs

⇒λ = ln2/5

now using formula, t = 1/λ ln[a/(a - x)]

= 5/ln2 ln[6.023 × 10²³/(6.023 - 4.515) × 10²³ ]

= 5/ln2 ln(4/1)

= 5ln(4)/ln2

= 10 hrs

hence 10 hrs would take for 4.515 × 10²³ alpha particles to be stored in that vessel.