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Question

If Tungsten undergoes alpha decay, what element does it transmute into? Show abalanced nuclear reaction equation to demonstrate how to find the answer. The equationis set up for you, but you will need to replace the A, X, & Z for both the alpha particleand the new element.
To answer, change each of the Z, A and X values below to make the equation balanced.
74
184
W→X
A Z +X
A Z

Answer 1

In alpha decay, an element emits an alpha particle, which consists of 2 protons and 2 neutrons. An alpha particle can be represented as \(^4_2\text{He}\) (with 2 protons (Z) and a mass number (A) of 4).

For Tungsten (\(^{184}_{74}\text{W}\)), when it undergoes alpha decay, it will transmute into another element, changing both its atomic number and mass number.

Here's how to balance the nuclear reaction equation:

1. Initial Element: Tungsten (\(^{184}_{74}\text{W}\))
2. Alpha Particle: \(^4_2\text{He}\)
3. Final Element: We need to determine the new element's mass number (A) and atomic number (Z) after decay.

The formula for alpha decay can be written as:

\[ ^{A}{Z}\text{W} \rightarrow ^{A'}{Z'}\text{X} + ^{4}_{2}\text{He} \]

Where \(A\) is the mass number, \(Z\) is the atomic number, and \(X\) is the new element formed.

Balancing the equation:

• For tungsten:
  • Mass number (A) = 184
  • Atomic number (Z) = 74

For the alpha particle:

• Mass number (A) = 4
• Atomic number (Z) = 2

To find the new element:

1. New Mass Number: \[ A' = A - 4 = 184 - 4 = 180 \]
2. New Atomic Number: \[ Z' = Z - 2 = 74 - 2 = 72 \]

The element with atomic number 72 is Hafnium (Hf).

Final equation:

Putting everything together, the balanced nuclear reaction for the alpha decay of Tungsten can be written as:

\[ ^{184}{74}\text{W} \rightarrow ^{180}{72}\text{Hf} + ^{4}_{2}\text{He} \]

So, in this case, element \(X\) is Hafnium, with \(A = 180\) and \(Z = 72\). The final equation is:

\[ ^{184}{74}\text{W} \rightarrow ^{180}{72}\text{Hf} + ^{4}_{2}\text{He} \]