Step 1: Understand the question.
We must name the nanoparticle that sunscreen lotions actually use to protect skin from the sun.
Step 2: Think about what a sunscreen needs to do.
A sunscreen has to soak up or scatter the harmful ultraviolet (UV) rays of the sun. So the active material must be a good UV blocker.
Step 3: Check the metal options.
Gold, platinum (Pt) and palladium (Pd) are costly metals used mostly in jewellery, catalysis and electronics. They are not used to block UV light in creams, so we can drop them.
Step 4: Look at the oxide option.
Titanium dioxide ($\text{TiO}_2$) is a white semiconductor oxide that absorbs and scatters UV rays very well. Zinc oxide does the same job.
Step 5: See why the nano form is special.
When $\text{TiO}_2$ is ground down to nano size, it stops looking white and turns clear to the eye, yet it still blocks UV. That is why modern sunscreens do not leave a chalky white layer on the skin.
Step 6: Choose the answer.
So the nanoparticle in sunscreen is $\text{TiO}_2$, which is option (C).
\[ \boxed{\text{TiO}_2} \]