Population at Time t Calculator

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✖Number of Particles in Sample Initially is the total number of particles in the sample present initially.ⓘ Number of Particles in Sample Initially [N_o]			+10% -10%
✖The decay constant is its probability of decay per unit time.ⓘ Decay Constant [λ]			+10% -10%
✖Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.ⓘ Time [t]			+10% -10%

✖Number of Particles at Time t is the total number of particles remaining in the sample after decay.ⓘ Population at Time t [N_t]

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Formula

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Population at Time t

Formula

`"N"_{"t"} = "N"_{"o"}*e^(-("λ"*"t")/(3.156*10^7))`

Example

`"49.99998"="50"*e^(-("0.4Hz"*"25s")/(3.156*10^7))`

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Population at Time t Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7))
N_t = N_o*e^(-(λ*t)/(3.156*10^7))
This formula uses 1 Constants, 4 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Number of Particles at Time t - Number of Particles at Time t is the total number of particles remaining in the sample after decay.
Number of Particles in Sample Initially - Number of Particles in Sample Initially is the total number of particles in the sample present initially.
Decay Constant - (Measured in Hertz) - The decay constant is its probability of decay per unit time.
Time - (Measured in Second) - Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

STEP 1: Convert Input(s) to Base Unit

Number of Particles in Sample Initially: 50 --> No Conversion Required
Decay Constant: 0.4 Hertz --> 0.4 Hertz No Conversion Required
Time: 25 Second --> 25 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

N_t = N_o*e^(-(λ*t)/(3.156*10^7)) --> 50*e^(-(0.4*25)/(3.156*10^7))

Evaluating ... ...

N_t = 49.9999841571635

STEP 3: Convert Result to Output's Unit

49.9999841571635 --> No Conversion Required

FINAL ANSWER

49.9999841571635 ≈ 49.99998 <-- Number of Particles at Time t

(Calculation completed in 00.004 seconds)

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Created by Anshika Arya

National Institute Of Technology (NIT), Hamirpur

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Verified by Rushi Shah

K J Somaiya College of Engineering (K J Somaiya), Mumbai

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< 11 Nucleus Calculators

Binding Energy

Go Binding Energy = (Atomic Number*Mass of Proton+(Mass Number-Atomic Number)*Mass of Neutron-Mass of Atom)*[c]^2

Mass Defect

Go Mass Defect = Atomic Number*Mass of Proton+(Mass Number-Atomic Number)*Mass of Neutron-Mass of Atom

Population at Time t

Go Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7))

Population after N Half Lives

Go Number of Particles at Time t = Number of Particles in Sample Initially/(2^(Number of Half Lives))

Decay Rate

Go Decay Rate = -Decay Constant*Total Number of Particles in Sample

Nuclear Radius

Go Nuclear Radius = Radius of Nucleon*Mass Number^(1/3)

Change in Mass in Nuclear Reaction

Go Mass Defect = Mass Reactant-Mass Product

Q-Value

Go Q Value = Initial Energy-Final Energy

Half Life for Nuclear Decay

Go Half Life Period = 0.693/Decay Constant

Average Life

Go Average Life = 1/Decay Constant

Energy Released in Nuclear Reaction

Go Energy = Mass Defect*[c]^2

Population at Time t Formula

Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7))
N_t = N_o*e^(-(λ*t)/(3.156*10^7))

How is radioactive decay measured?

Those that decay are called radioactive (or parent) isotopes; those that are generated by decay are called radiogenic (or daughter) isotopes. The unit that we use to measure time is called half-life and it has to do with the time it takes for half of the radioactive isotopes to decay.

How to Calculate Population at Time t?

Population at Time t calculator uses Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)) to calculate the Number of Particles at Time t, The Population at Time t formula is defined as total number of particles remaining in the sample after nuclear decay. Number of Particles at Time t is denoted by N_t symbol.

How to calculate Population at Time t using this online calculator? To use this online calculator for Population at Time t, enter Number of Particles in Sample Initially (N_o), Decay Constant (λ) & Time (t) and hit the calculate button. Here is how the Population at Time t calculation can be explained with given input values -> 49.99998 = 50*e^(-(0.4*25)/(3.156*10^7)).

FAQ

What is Population at Time t?

The Population at Time t formula is defined as total number of particles remaining in the sample after nuclear decay and is represented as N_t = N_o*e^(-(λ*t)/(3.156*10^7)) or Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)). Number of Particles in Sample Initially is the total number of particles in the sample present initially, The decay constant is its probability of decay per unit time & Time is the continued sequence of existence and events that occurs in an apparently irreversible succession from the past, through the present, into the future.

How to calculate Population at Time t?

The Population at Time t formula is defined as total number of particles remaining in the sample after nuclear decay is calculated using Number of Particles at Time t = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)). To calculate Population at Time t, you need Number of Particles in Sample Initially (N_o), Decay Constant (λ) & Time (t). With our tool, you need to enter the respective value for Number of Particles in Sample Initially, Decay Constant & Time and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Number of Particles at Time t?

In this formula, Number of Particles at Time t uses Number of Particles in Sample Initially, Decay Constant & Time. We can use 1 other way(s) to calculate the same, which is/are as follows -

Number of Particles at Time t = Number of Particles in Sample Initially/(2^(Number of Half Lives))

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