Chapter 20, Problem 16E

(a)

Interpretation Introduction

Interpretation:

The unknown element for equation for $?+He\to Bk+n$ needs to be determined.

Concept Introduction:

A radioactive decay is unstable nuclei which undergoes decay as it dissociates to smaller fragments releasing alpha, beta or gamma particles. This is because the ratio of number of protons to number of neutrons is not equal. If the ratio of number of protons to number of neutrons is less or equal to 1, then positron is released and if the ratio is more than 1 then beta particle is released.

Answer to Problem 16E

The unknown element for equation $?+He\to Bk+n$ is $Am$ .

Explanation of Solution

The equation given is $?+He\to Bk+n$

To determine the mass number and atomic number of unknown elements, the mass numbers and atomic numbers are equated on both sides.

  $\begin{array}{c}\text{Mass number : ? + 4 = 243 + 1}\\ x=244-4=240\\ \text{Atomic number : }x\text{ + 2 = 97 + 0}\\ x=97-2\\ =95\end{array}$

Looking through the periodic table, the element with mass number 240 and atomic number 95 is $Am$ .

The equation is written as $Am+He\to Bk+n$ .

(b)

Interpretation Introduction

Interpretation:

The unknown element for equation for $U+C\to ?+6n$ needs to be determined.

Concept Introduction:

An unstable nuclei which undergo decay to dissociate to smaller fragments releasing alpha, beta or gamma particles as there is an imbalance in the ratio of number of protons to number of neutrons. If the ratio of number of protons to number of neutrons is less or equal to 1, then positron is released and if the ratio is more than 1 then beta particle is released.

Answer to Problem 16E

The unknown element for equation $U+C\to ?+6n$ is $Cf$ .

Explanation of Solution

The equation given is $U+C\to ?+6n$

To determine the mass number and atomic number of unknown elements, the mass numbers and atomic numbers are equated on both sides.

  $\begin{array}{c}\text{Mass number : 238 + 12 = ? + 6}\\ x=250-6=244\\ \text{Atomic number : }92\text{ + 6 = ?+ 0}\\ x=98-0\\ =98\end{array}$

Looking through the periodic table, the element with mass number 244 and atomic number 98 is $Cf$ .

The equation is written as $U+C\to Cf+6n$ .

(c)

Interpretation Introduction

Interpretation:

The unknown element for equation for $Cf+?\to Db+\text{ 4}n$ needs to be determined.

Concept Introduction:

A radioactive decay undergoes when an unstable nuclei dissociates to smaller fragments releasing alpha, beta or gamma particles due to imbalance in the number of protons to number of neutrons If the ratio of protons to number of neutrons is less or equal to 1, a positron is released and if the ratio is more than 1 then there is release of beta particle.

Answer to Problem 16E

The unknown element for equation $Cf+?\to Db+\text{ 4}n$ is $N$ .

Explanation of Solution

The equation given is $Cf+?\to Db+\text{ 4}n$

To determine the mass number and atomic number of unknown elements, the mass numbers and atomic numbers are equated on both sides.

  $\begin{array}{c}\text{Mass number : 249 + ? = 260 + 4}\\ x=264-249=15\\ \text{Atomic number : }98\text{ + ? = 105+ 0}\\ x=105-98\\ =7\end{array}$

Looking through the periodic table, the element with mass number 15 and atomic number 7 is $N$ .

The equation is written as $Cf+N\to Db+\text{ 4}n$ .

(d)

Interpretation Introduction

Interpretation:

The unknown element for equation for $Cf+B\to Lr+?$ needs to be determined.

Concept Introduction:

If nucleus is unstable, it will undergo dissociation such that it dissociates to smaller fragments releasing alpha, beta or gamma particles. The instability is due to an imbalance in the ratio of number of protons to number of neutrons. If the ratio of number of protons to number of neutrons is less or equal to 1, then positron is released and if the ratio is more than 1 then beta particle is released.

Answer to Problem 16E

The unknown element for equation $Cf+B\to Lr+?$ is $\text{2}n$ .

Explanation of Solution

The equation given is $Cf+B\to Lr+?$

To determine the mass number and atomic number of unknown elements, the mass numbers and atomic numbers are equated on both sides.

  $\begin{array}{c}\text{Mass number : 249 + 10 = 257 + ?}\\ x=259-257=2\\ \text{Atomic number : }98\text{ + 5 = 103+ ?}\\ x=103-103\\ =0\end{array}$

Looking through the periodic table, the element with mass number 2 and atomic number 0 is $\text{2}n$ .

The equation is written as $Cf+B\to Lr+\text{ 2}n$ .