Question

In which of the following reactions or decays is strangeness conserved? In each case, explain your reasoning.

$\mathbf{\left(}\mathbf{a}\mathbf{\right)}{\mathbf{K}}^{\mathbf{+}}\mathbf{\to }{\mathit{\mu }}^{\mathbf{+}}\mathbf{+}{\mathit{\nu }}_{\mathbf{\mu }}\mathbf{;}$

$\mathbf{\left(}\mathbf{b}\mathbf{\right)}\mathit{n}\mathbf{+}{\mathit{K}}^{\mathbf{+}}\mathbf{\to }\mathit{p}\mathbf{+}{\mathit{\pi }}^{\mathbf{0}}\mathbf{;}$

$\mathbf{\left(}\mathbf{\text{c}}\mathbf{\right)}{\mathit{K}}^{\mathbf{+}}\mathbf{+}{\mathit{K}}^{\mathbf{-}}\mathbf{\to }{\mathit{\pi }}^{\mathbf{0}}\mathbf{+}{\mathit{\pi }}^{\mathbf{0}}\mathbf{;}$

$\mathbf{\left(}\mathbf{\text{d}}\mathbf{\right)}\mathit{p}\mathbf{+}{\mathit{K}}^{\mathbf{-}}\mathbf{\to }{\mathit{\Lambda }}^{\mathbf{0}}\mathbf{+}{\mathit{\pi }}^{\mathbf{0}}\mathbf{.}$

Short answer

The reactions$\left(c\right),\left(d\right)$are strangeness conserved

Step-by-step solution

Define Strangeness

The K mesons and the ${\mathit{\Lambda }}^{\mathbf{0}}$and $\mathit{\Sigma }$hyperons are called the strange particles.

Strangeness is conserved in strong interactions, but it can change by 0 or 1.

Given information

Table representing strangeness quantum number of strange particles:

Strange particles	Strangeness quantum number
$K^{+}$	$+1$
$K^{-}$	$-1$
${\Lambda }^0$	$-1$
$p$	$0$
${\pi }^0$	$0$
$n$	$0$
${\mu }^{+}$	0
${\nu }_{\mu }$	0

Check strangeness

a)

${\mathbf{K}}^{+}\to {\mu }^{+}+{\nu }_{\mu }$

The strangeness of each side is:

For LHS =$+1$

And

for RHS$=0$

Since both sides are not equal, therefore, the reaction is not strangeness conserved.

b)

$n+K^{+}\to p+{\pi }^0$

The strangeness of each side is:

For LHS $=+1$

And

for RHS $=0$

Since both sides are not equal, therefore, the reaction is not strangeness conserved.

c)

$K^{+}+K^{-}\to {\pi }^0+{\pi }^0$

The strangeness of each side is:

For LHS $=0$

And

for RHS $=0$

Since both sides are equal, therefore, the reaction is strangeness conserved.

d)

$p+K^{-}\to {\Lambda }^0+{\pi }^0$

The strangeness of each side is:

For LHS $=-1$

And

for RHS $=-1$

Since both sides are equal, therefore, the reaction is strangeness conserved.

Hence, the reactions $\left(c\right),\left(d\right)$are strangeness conserved.