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QuestionFind the mass of a 49Be{ }_{4}^{9} \mathrm{Be} nucleus using neutron (1.00867 amu) and proton (1.00728 amu) masses.

Studdy Solution

STEP 1

Assumptions1. The nucleus of 49Be{ }_{4}^{9} \mathrm{Be} has4 protons and5 neutrons (since the atomic number is4 and the atomic mass number is9). . The mass of a neutron is1.00867 amu.
3. The mass of a proton is1.00728 amu.
4. The mass of the nucleus is the sum of the masses of the protons and neutrons.

STEP 2

First, we need to calculate the total mass of the protons in the nucleus. We can do this by multiplying the number of protons by the mass of a single proton.
Massprotons=Numberprotons×Masssingle protonMass_{protons} = Number_{protons} \times Mass_{single\,proton}

STEP 3

Now, plug in the given values for the number of protons and the mass of a single proton to calculate the total mass of the protons.
Massprotons=×1.00728 amuMass_{protons} = \times1.00728\, amu

STEP 4

Calculate the total mass of the protons.
Massprotons=4×1.00728 amu=4.02912 amuMass_{protons} =4 \times1.00728\, amu =4.02912\, amu

STEP 5

Next, we need to calculate the total mass of the neutrons in the nucleus. We can do this by multiplying the number of neutrons by the mass of a single neutron.
Massneutrons=Numberneutrons×Masssingle neutronMass_{neutrons} = Number_{neutrons} \times Mass_{single\,neutron}

STEP 6

Now, plug in the given values for the number of neutrons and the mass of a single neutron to calculate the total mass of the neutrons.
Massneutrons=5×1.00867 amuMass_{neutrons} =5 \times1.00867\, amu

STEP 7

Calculate the total mass of the neutrons.
Massneutrons=5×1.00867 amu=5.04335 amuMass_{neutrons} =5 \times1.00867\, amu =5.04335\, amu

STEP 8

Now that we have the total mass of the protons and the total mass of the neutrons, we can find the total mass of the nucleus. This is the sum of the mass of the protons and the mass of the neutrons.
Massnucleus=Massprotons+MassneutronsMass_{nucleus} = Mass_{protons} + Mass_{neutrons}

STEP 9

Plug in the values for the mass of the protons and the mass of the neutrons to calculate the total mass of the nucleus.
Massnucleus=4.02912 amu+5.04335 amuMass_{nucleus} =4.02912\, amu +5.04335\, amu

STEP 10

Calculate the total mass of the nucleus.
Massnucleus=4.02912 amu+5.04335 amu=9.07247 amuMass_{nucleus} =4.02912\, amu +5.04335\, amu =9.07247\, amuThe mass of the 49Be{ }_{4}^{9} \mathrm{Be} nucleus is9.07247 amu.

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