✖Number of Particles in Sample Initially is the quantity of particles present in a sample at the beginning of a nuclear reaction or process.ⓘ Number of Particles in Sample Initially [N_o]			+10% -10%
✖Decay Constant is a measure of the rate at which unstable atoms undergo radioactive decay, emitting ionizing radiation, and is a fundamental concept in nuclear physics and chemistry.ⓘ Decay Constant [λ]			+10% -10%
✖Time is the duration between two events, typically measured in seconds, minutes, hours, or years, and is a fundamental concept in physics, engineering, and everyday life.ⓘ Time [t]			+10% -10%

✖Number of Particles at Time is the quantity of particles present at a specific time t in a nuclear reaction, providing insight into the reaction's progression and dynamics.ⓘ Population at Time [N_t]

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Formula

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Population at Time

Formula

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

Example

`"50.09998"="50.1"*e^(-("0.4Hz"*"25s")/(3.156*10^7))`

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Population at Time Solution

STEP 0: Pre-Calculation Summary

Formula Used

Number of Particles at Time = 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 - Number of Particles at Time is the quantity of particles present at a specific time t in a nuclear reaction, providing insight into the reaction's progression and dynamics.
Number of Particles in Sample Initially - Number of Particles in Sample Initially is the quantity of particles present in a sample at the beginning of a nuclear reaction or process.
Decay Constant - (Measured in Hertz) - Decay Constant is a measure of the rate at which unstable atoms undergo radioactive decay, emitting ionizing radiation, and is a fundamental concept in nuclear physics and chemistry.
Time - (Measured in Second) - Time is the duration between two events, typically measured in seconds, minutes, hours, or years, and is a fundamental concept in physics, engineering, and everyday life.

STEP 1: Convert Input(s) to Base Unit

Number of Particles in Sample Initially: 50.1 --> 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)) --> 50.1*e^(-(0.4*25)/(3.156*10^7))

Evaluating ... ...

N_t = 50.0999841254778

STEP 3: Convert Result to Output's Unit

50.0999841254778 --> No Conversion Required

FINAL ANSWER

50.0999841254778 ≈ 50.09998 <-- Number of Particles at Time

(Calculation completed in 00.004 seconds)

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< 11 Nuclear Physics Calculators

Binding Energy

Go 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

Go Number of Particles at Time = 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 = 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 Formula

Number of Particles at Time = 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))

What is radiation?

Radiation is the emission and transmission of energy in the form of waves or particles. It is classified into two main types: ionizing radiation, which has enough energy to remove electrons from atoms and can cause damage to living tissue, and non-ionizing radiation, which lacks sufficient energy to ionize atoms.

How to Calculate Population at Time?

Population at Time calculator uses Number of Particles at Time = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)) to calculate the Number of Particles at Time, Population at Time formula is defined as a measure of the number of individuals in a population at a specific point in time, taking into account the initial population size and the rate of decline or growth over time, providing valuable insights into population dynamics and growth patterns. Number of Particles at Time is denoted by N_t symbol.

How to calculate Population at Time using this online calculator? To use this online calculator for Population at Time, 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 calculation can be explained with given input values -> 50.09998 = 50.1*e^(-(0.4*25)/(3.156*10^7)).

FAQ

What is Population at Time?

Population at Time formula is defined as a measure of the number of individuals in a population at a specific point in time, taking into account the initial population size and the rate of decline or growth over time, providing valuable insights into population dynamics and growth patterns and is represented as N_t = N_o*e^(-(λ*t)/(3.156*10^7)) or Number of Particles at Time = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)). Number of Particles in Sample Initially is the quantity of particles present in a sample at the beginning of a nuclear reaction or process, Decay Constant is a measure of the rate at which unstable atoms undergo radioactive decay, emitting ionizing radiation, and is a fundamental concept in nuclear physics and chemistry & Time is the duration between two events, typically measured in seconds, minutes, hours, or years, and is a fundamental concept in physics, engineering, and everyday life.

How to calculate Population at Time?

Population at Time formula is defined as a measure of the number of individuals in a population at a specific point in time, taking into account the initial population size and the rate of decline or growth over time, providing valuable insights into population dynamics and growth patterns is calculated using Number of Particles at Time = Number of Particles in Sample Initially*e^(-(Decay Constant*Time)/(3.156*10^7)). To calculate Population at Time, 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?

In this formula, Number of Particles at Time 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 = Number of Particles in Sample Initially/(2^(Number of Half Lives))

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