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I wanted to say "I'm going to take a nap for a while" and looked for the phrase "(for) a while" in Chinese and came across these 5 :
一会，一下，一时，一时半会，片刻。

Could you please tell me the difference between those five?

Will there be any difference if I say :

我要去小睡一会

我要去小睡一下

我要去小睡一时

我要去小睡一时半会

我要去小睡片刻

???

And last, does adding "儿" to 一会/一下 change the meaning?

Thank you in advance!!!

(Ps : I'm a beginner in Chinese. I'm sorry if my question sounds silly or something. Also, it'd be very helpful if you could provide some examples while explaining things so I can understand better).

You would say

我要去小睡片刻 or 我要去小睡一会儿

Other expressions you have are not normally used.

You could also say

我要稍微睡一会儿

All the phrases you have can refer to a short interval of time in certain context, but they can have different meanings, 一下

一下，a short interval of time, for example, 灯一下又亮了

一下，once, for example, 你过去打他一下

一下，sudden, for example, 天一下就黑了

一时 has the following meanings

一时，a short interval of time, for example, 你别一时想不开

一时，a period of time, for example, 此一时彼一时

一时，at the same time, for example, 一时间，箭、弩都发射出去

And the others

一会，a short interval of time, for example, 我要出去一会

一时半会（儿），a short interval of time, for example, 他们一时半会儿还回不来

片刻，a short interval of time, for example, 请稍等片刻

I am only listing the common meanings and although they could have same meaning, the way you use them could be different and that is why I included the examples.

Adding 儿 after 一会 would not change its meaning, it just sounds more natural and is highly recommended. However, there is no such use of adding 儿 after 一下。

No difference, It is about what sayings are more popular than the others. it could depend on where you came from(different education level and/or region).