A certain radioactive nucleus emits a gamma ray with an energy of 0.186 MeV.
Calculate the mass lost by the nucleus during the decay process.
E=mc^2
.186e6 ev* 1.60218e-19j/ev=m*3e8m/s
solve for m in kg
Well, you know what they say - it's all about losing that mass and feeling light!
To calculate the mass lost by the nucleus during the decay process, we can use Einstein's famous equation: E = mc². Here, E represents the energy emitted, m represents the mass lost, and c is the speed of light.
Now, we need to convert the energy from MeV to joules, since the equation requires SI units. Using the conversion factor 1 MeV = 1.602 × 10⁻¹³ J, we find that the energy emitted is 0.186 MeV = 0.186 × 1.602 × 10⁻¹³ J.
Next, we rearrange the equation to solve for mass: m = E / c². The speed of light, c, is approximately 3 × 10⁸ m/s, so we substitute that in.
m = (0.186 × 1.602 × 10⁻¹³ J) / (3 × 10⁸ m/s)².
After crunching the numbers, I find that the mass lost by the nucleus during the decay process is approximately 3.29 × 10⁻²⁷ kg.
So, the nucleus lost some weight, but don't worry, it's still a heavy subject!
To calculate the mass lost by the nucleus during the decay process, we can use Einstein's famous equation: E = mc^2, where E is the energy lost, m is the mass lost, and c is the speed of light.
First, let's convert the energy from MeV to Joules. 1 MeV is equal to 1.602 x 10^-13 Joules.
Given that the energy emitted by the nucleus is 0.186 MeV, we can calculate the energy in Joules:
0.186 MeV x 1.602 x 10^-13 J/MeV = 2.98 x 10^-14 J
Now we can rearrange the equation E = mc^2 to solve for m:
m = E / c^2
Plugging in the values:
m = 2.98 x 10^-14 J / (3 x 10^8 m/s)^2
m = 2.98 x 10^-14 J / 9 x 10^16 m^2/s^2
m = 3.31 x 10^-31 kg
Therefore, the mass lost by the nucleus during the decay process is approximately 3.31 x 10^-31 kg.
To calculate the mass lost by the nucleus during the decay process, we can use Einstein's famous equation, E=mc², where E is the energy released, m is the mass lost, and c is the speed of light.
First, let's convert the energy of the gamma ray from MeV (mega-electron volts) to joules, using the conversion factor 1 MeV = 1.6 x 10⁻¹³ Joules.
0.186 MeV * (1.6 x 10⁻¹³ J/1 MeV) = 2.976 x 10⁻¹⁴ J
Next, we can use the equation E=mc² to solve for m.
m = E/c²
Now, substitute the values:
m = 2.976 x 10⁻¹⁴ J / (2.998 x 10⁸ m/s)²
m ≈ 3.322 x 10⁻³² kg
Therefore, the mass lost by the nucleus during the decay process is approximately 3.322 x 10⁻³² kg.