Half-life and radioactive decay calculator

Half-life calculator: amount left, starting amount, elapsed time or half-life from N = N₀·2^(−t/t½), with carbon-14 and other isotope presets.

হালনাগাদ ২৮ সেপ্টেম্বর, ২০২৬যাচাই করা উদাহরণ: ৮

Amount left N

সার্থক অঙ্ক: ৬; নিকটতম; সমান দূরত্বে শূন্য থেকে দূরে

অর্ধায়ু: 5,700yr / 2,081,880d
Fraction remaining: 50%
Half-lives elapsed: 1
Decay constant λ: 3.8535 × 10⁻¹²1/s
Mean lifetime τ = 1/λ: 8,223.36yr

Years are Gregorian average years (365.2425 d). Carbon-14: t½ = 5700 years (NNDC), used for radiocarbon dating.

After 1 half-life (5,700 years), 50% of Carbon-14 remains: 50 of 100.

Decay of Carbon-14

যেভাবে হিসাব করা হয় S

Half-life in seconds
$t_{1/2} = 179{,}875{,}000{,}000\ \mathrm{s} = 5{,}700\ \mathrm{yr}$
Amount left
$N = N_0\,2^{-t/t_{1/2}} = 100\times 2^{-1} = 50$
Decay constant and mean lifetime
$\lambda = \frac{\ln 2}{t_{1/2}} = 3.8535 \times 10^{-12}\ \mathrm{s^{-1}},\quad \tau = \frac1\lambda = 8{,}223.36\ \mathrm{yr}$

Half-life and radioactive decay calculator সম্পর্কে

Radioactive material decays exponentially: after each half-life t½ half of the remaining nuclei are left, so N = N₀·2^(−t/t½), or N₀e^(−λt) with decay constant λ = ln 2/t½. Enter any three of starting amount, amount left, elapsed time and half-life to get the fourth, along with the fraction remaining, the number of half-lives and the mean lifetime 1/λ.

The default, 100 g of carbon-14 after 5,700 years, leaves 50 g: one half-life. Radiocarbon dating runs the same equation backwards, so a sample with 25% of the carbon-14 in living tissue is two half-lives, or 11,400 years, old. After 30 days, 7.49% of an iodine-131 dose remains.

Half-lives come from the NNDC NuDat 3 database. Amounts can be in any unit (grams, atoms, becquerels or percent) as long as both use the same one. Published radiocarbon ages use the Libby half-life of 5,568 years by convention and are then calibrated, so they differ from this raw calculation.

সমাধান করা উদাহরণ

Carbon-14 after one half-life

Solve for: Amount left
Isotope: Carbon-14
Starting amount N₀: 100
Elapsed time: 5700 yr

Amount left N: 50
Half-lives elapsed: 1

যাচাইয়ের উৎস: Definition of half-life (t½ = 5700 y, NNDC)

Radiocarbon age at 25% remaining

Solve for: সময়
Isotope: Carbon-14
Starting amount N₀: 100
Amount left N: 25

Elapsed time: 11,400 yr
Half-lives elapsed: 2

যাচাইয়ের উৎস: Two half-lives: 2 × 5700 y

Iodine-131 after 30 days

Solve for: Amount left
Isotope: Iodine-131
Starting amount N₀: 100
Elapsed time: 30 d

Amount left N: 7.49346

যাচাইয়ের উৎস: Python 3.8 decimal: 100 × 2^(−30/8.0252) = 7.4934578

Half-life from 1000 → 125 counts in 30 min

Solve for: অর্ধায়ু
Starting amount N₀: 1000
Amount left N: 125
Elapsed time: 30 min

অর্ধায়ু: 0.006944 d
Half-lives elapsed: 3

যাচাইয়ের উৎস: Python 3.8 decimal: t½ = 30 ln2 / ln 8 = 10 min = 0.0069444 d

প্রশ্ন

How do you calculate half-life?

t½ = t·ln 2/ln(N₀/N), from a starting amount N₀ and the amount N left after time t. If a count rate falls from 1,000 to 125 in 30 minutes, N₀/N = 8 = 2³, so three half-lives have passed and t½ = 10 minutes. The logarithm handles any ratio: 1,000 falling to 300 in 30 minutes gives t½ = 17.3 minutes.

How much is left after 3 half-lives?

12.5%. Each half-life halves what remains: 50% after one, 25% after two, 12.5% after three and 6.25% after four. After n half-lives the fraction left is (1/2)ⁿ, so falling to 1% takes 6.64 half-lives and falling below 0.1% takes 10 (0.098% remains).

What is the half-life of carbon-14?

5,700 years in the evaluated nuclear data published by the NNDC; older textbooks give 5,730 years. Radiocarbon dating reaches back about 50,000 years, close to nine half-lives, after which less than 0.3% of the original carbon-14 remains, too little to measure reliably.

What is the difference between half-life and mean lifetime?

Mean lifetime τ is the average time a nucleus survives before it decays: τ = 1/λ = t½/ln 2 ≈ 1.443 t½. For carbon-14 that is 5,700/0.693 = 8,223 years. After one mean lifetime 1/e, or 36.8%, of the sample remains, compared with 50% after one half-life.

What is the decay constant?

λ = ln 2/t½, the probability per unit time that a given nucleus decays. It links amount to activity through A = λN, in becquerels when N counts atoms and λ is per second. Carbon-14's λ is 3.85 × 10⁻¹² per second, so 1 g of pure carbon-14, 4.3 × 10²² atoms, has an activity of about 1.66 × 10¹¹ Bq.

“Half-life and radioactive decay calculator” কতটা নির্ভুল?

নির্ভুলতা আপনার ইনপুট ও পদ্ধতির অনুমানের ওপর নির্ভর করে। দশমিক গণনায় 50টি সার্থক অঙ্ক ব্যবহৃত হয়, কিন্তু আনুমানিক হিসাব, সংখ্যাগত পদ্ধতি ও উৎসের তথ্য কম নির্ভুল হতে পারে; প্রদর্শিত মান রাউন্ড করলে এই সীমাবদ্ধতাগুলি দূর হয় না। স্বতন্ত্র উৎসের সমাধানের সঙ্গে যাচাই করা উদাহরণ: ৮। যেমন, “Carbon-14 after one half-life” উদাহরণটি Definition of half-life (t½ = 5700 y, NNDC)-এর সঙ্গে যাচাই করা হয়।

এই পদ্ধতির উৎস কী?

NNDC NuDat 3 (ENSDF evaluated half-lives), Brookhaven National Laboratory; OpenStax University Physics Volume 3, §10.3 Radioactive decay.

এই ক্যালকুলেটর সম্পর্কে

N = N_0\,2^{-t/t_{1/2}} = N_0e^{-\lambda t},\qquad \lambda = \frac{\ln 2}{t_{1/2}},\qquad \tau = \frac1\lambda

উৎস

তথ্যসূত্রের সঙ্গে যাচাই করা

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