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What is the usage of the 2nd "of" in this sentence?

the duration of the x-ray pulse can be of picosecond duration

Why is it not be this?

the duration of the x-ray pulse can be picosecond

Is there a difference in the meaning between the two? Thanks in advance

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    Can be picosecond is ungrammatical. You can't just remove of. It's fine as it is; otherwise, it needs to be replaced by something else. – Jason Bassford Apr 21 '19 at 16:42
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I believe the difference is the duration.

the x-ray pulse can be of picosecond duration

this means, that the duration can be measured in picoseconds as compared to minutes or hours. It could be 1.0 ps or 0.7 ps, 5.8 ps, 12.9 ps...

the duration of the x-ray pulse can be picosecond

like Philip Wood said, this sentence is not exactly correct. It could either be missing "a" or "-s".

the duration of the x-ray pulse can be a picosecond - it can be exactly 1.0 ps

the duration of the x-ray pulse can be picoseconds - it is measured in picoseconds

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    Thanks. So to make the 2nd sentence to mean like the 1st one, the last part of the 2nd sentence would be "a picosecond or picoseconds" or "picoseconds order" or "around picoseconds" . am I right? – Hayashi Yoshiaki Apr 22 '19 at 8:15
  • In case of "a picosecond or picoseconds" there's no point in mentioning the single picosecond, so I'd just use "picoseconds". The thing is that in "picosecond duration" the word "picosecond" is an adjective. The best way to write the second sentence would be "The duration of the x-ray pulse can be measured in picoseconds". The options "picoseconds order" or "around picoseconds" are incorrect. – Lassy Apr 22 '19 at 11:36
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Here are two ways of making the statement:

(a) The X-ray pulse can be of a picosecond duration.

(b) The duration of the X-ray pulse can be a picosecond.

The second of the sentences you quote, needs 'a' before picosecond. It is then identical to (b).

The first of the sentences that you quote mixes elements from (a) and (b) unsuccessfully. It repeats 'duration' unnecessarily – and so distracts the reader.

"of a picosecond duration" in (a) is an adjectival phrase qualifying "X-ray pulse", in the same way that we might describe someone as being "of a kindly nature". [I'm not convinced that 'of' in this context indicates possession.]

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You've stumbled here on a proper English idiom which may (for all I know) be unusual or unique to English, which occurs a lot, and to use which marks one out as fluent.

It's a way of predicating a quality or attribute of a thing or person, using the preposition "of". As always, the paradigm is in the Authorized Version of the Bible: "He is ... a man of sorrows... " (Isaiah 53.3). The form is "N is a [noun1] of [noun2]" - where noun2 is a quality or attribute which noun1 possesses.

(So right here you have two distinctive features of English: lots of work done by idiomatic use of prepositions; word order critical to sense.)

The attribute is very often a noun phrase - "a woman of a certain age" / "a horse of a different colour". And that's what you're dealing with here. The sentence in question is a bit clunky, because "picosecond" is being used as an adjective but doesn't have the form of an adjective.

It's also ambiguous, because if you gloss "picosecond" as "picosecond-long" it means the pulse can be one picosecond; if you gloss it as "measured-in-picoseconds" then it could be anything from 0.1 (below which you'd probably talk in femtoseconds) to at least 99 (after which you might start talking tenths of a nano-second).

So, not a nice sentence, but a way into a wonderful linguistic world.

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