# Half-Life Calculator

Given Half-Life Calculator is useful to find the half-life, decay constant, initial and final amount of substance easily. Just provide inputs i.e initial quantity, final quantity, total time and click the blue colour calculate button to check the half-time in a less amount of time.

### Step by Step Process to Find Half-Life

Check out the simple steps to calculate the radioactive substance half-life.

- Obtain the initial quantity, total time and final quantity of the substance.
- Place the values in the Half-life formula.
- Solve the equation for the half-life to get the result.

### What is the Half-Life?

Half-life is a phenomenon that takes place daily in various chemical reactions and nuclear reactions. It is the amount of time it takes for half of a particle sample to react. In nuclear physics, the half-life represents the time taken by atoms to undergo radioactive decay.

Every atom has a different half-life. For example, uranium-233 has a half-life of 160,000 years. It is used to describe a kind of exponential decay. The half-life is a probabilistic measure and it can't give the exact half of the substance that will be decayed after the time of half-life has elapsed.

### Half-Life Formula

The number of unstable nuclei remaining after the time can be find using the Half-life formula

**N(t) = N(0) x 0.5(t/T)**

**N(t) = N(0) x e(-t/τ)**

**N(t) = N(0) x e(-λt)**

Where,

N(t) is the remaining amount of a substance after time t has elapsed

N(0) is the initial amount of the substance

T is the half-life

t is the full time

τ is the mean life time that is the average amount of time a nucleus remains intact

λ is the decay constant

**Example:**

**Question: Calculate the half-life of a radioactive substance whose disintegration constant is 0.002 1/years?**

Answer:

Given that,

Radioactive constant λ = 0.002 1/years

Half-life t½ = 0.693/λ

= 0.693/0.002

= 346.5 years

Therefore, the radioactive substance half-life is 346.5 years.

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### FAQ’s on pH Calculator

**1. What is meant by half-life?**

Half-life is nothing but the time required for a quantity to reduce to half of its initial value. It is generally used in nuclear physics to know how quickly unstable atoms will undergo radioactive decay.

**2. How to calculate the half-life without a calculator?**

Determine the initial quantity, final quantity of the substance, total time. Substitute these values in the half-life equation and solve to get the half-life of the substance.

**3. What is a Half-life formula?**

The number of unstable nuclei remaining after the time t can be calculated using the half-life equation. It is N(t) = N(0) x 0.5(t/T). Here, N(0) is the initial quantity of the substance, N(t) is the remaining quantity of the substance after t time, T is the half-life.

**4. Calculate the half-life of a radioactive substance whose disintegration constant is 0.004 1/years?**

Given that,

The decay constant of the radioactive substance = 0.004 1/years

The half-life formula is t½ = 0.693/λ

= 0.963/0.004

= 173.25

Therefore, the half-life of the radioactive substance is 173.25 years.