The number of molecules/ions that show linear geometry among the following is ______
$$ \mathrm{SO_2},\ \mathrm{BeCl_2},\ \mathrm{CO_2},\ \mathrm{N_3^-},\ \mathrm{NO_2},\ \mathrm{F_2O},\ \mathrm{XeF_2},\ \mathrm{NO_2^+},\ \mathrm{I_3^-},\ \mathrm{O_3} $$

We need to count the number of molecules/ions with linear geometry from the given list.

$$SO_2, BeCl_2, CO_2, N_3^-, NO_2, F_2O, XeF_2, NO_2^+, I_3^-, O_3$$

Analyzing each:

1. $$SO_2$$: S has 2 bonding pairs + 1 lone pair = bent geometry. NOT linear.

2. $$BeCl_2$$: Be has 2 bonding pairs, no lone pairs. sp hybridized. LINEAR.

3. $$CO_2$$: C has 2 double bonds, no lone pairs. sp hybridized. LINEAR.

4. $$N_3^-$$: Azide ion. Central N has 2 bonding regions, no lone pairs. sp hybridized. LINEAR.

5. $$NO_2$$: N has 2 bonding pairs + 1 unpaired electron = bent geometry. NOT linear.

6. $$F_2O$$: O has 2 bonding pairs + 2 lone pairs = bent geometry. NOT linear.

7. $$XeF_2$$: Xe has 2 bonding pairs + 3 lone pairs = LINEAR (sp³d hybridization, trigonal bipyramidal with F atoms in axial positions).

8. $$NO_2^+$$: Nitronium ion. N has 2 double bonds, no lone pairs. sp hybridized. LINEAR.

9. $$I_3^-$$: Central I has 2 bonding pairs + 3 lone pairs = LINEAR (similar to XeF₂).

10. $$O_3$$: Central O has 2 bonding regions + 1 lone pair = bent geometry. NOT linear.

Linear molecules/ions: $$BeCl_2, CO_2, N_3^-, XeF_2, NO_2^+, I_3^-$$ = 6

The answer is 6.