What is the half life of the element in the picture

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6 days

Explanation:

The following data were obtained from the question:

Original amount (N₀) = 100 mg

Amount remaining (N) = 6. 25 mg

Time (t) = 24 days

Half life (t½) =?

Next, we shall determine the decay constant. This can be obtained as follow:

Original amount (N₀) = 100 mg

Amount remaining (N) = 6. 25 mg

Time (t) = 24 days

Decay constant (K) =?

Log (N₀/N) = kt / 2.303

Log (100/6.25) = k × 24 / 2.303

Log 16 = k × 24 / 2.303

1.2041 = k × 24 / 2.303

Cross multiply

k × 24 = 1.2041 × 2.303

Divide both side by 24

K = (1.2041 × 2.303) / 24

K = 0.1155 /day

Finally, we shall determine the half-life of the isotope as follow:

Decay constant (K) = 0.1155 /day

Half life (t½) =?

t½ = 0.693 / K

t½ = 0.693 / 0.1155

t½ = 6 days

Therefore, the half-life of the isotope is 6 days

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