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My book (Comprehensive Chemistry by Dr. N . K. Verma, S. K. Khanna, Dr. B. Kapila) mentions two forms of hydrogen — "atomic" & "nascent".

It says that these two forms of hydrogen are more or less the same except that the former is produced by passing $\ce{H2}$ gas through an electric arc struck between two tungsten filaments and the latter is formed during chemical reactions in aqueous solutions. For example, $$\ce{Zn + H2SO4 -> ZnSO4 + 2[H]}$$

The book also said that the reactivity order of these hydrogens is

$$\ce{H2} \lt \ce{[H]} \lt \rm atomic~hydrogen$$

But I think that the reactivity of $\ce{[H]}$ must be same as atomic hydrogen. So please explain the difference between them and also their reactivity order.

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Is your book by chance very old? From the Wikipedia entry for "nascent hydrogen":

Nascent hydrogen is purported to consist of a chemically reactive form of hydrogen that is freshly generated, hence nascent. Molecular hydrogen ($\ce{H2}$), which is the normal form of this element, is unreactive toward organic compounds, so a special state of hydrogen was once invoked to explain certain kinds of hydrogenations. Mechanistic understanding of such reactions is now available, and the concept of nascent hydrogen is discounted, even ridiculed.

Then, by example of how this concept came to be:

Reductions of esters to give alcohols using a mixture of sodium and alcohols is called the Bouveault–Blanc reduction. It is an old reaction that has largely been superseded by alternative methods. At the time of popularity, the process caused much puzzlement because esters are unreactive toward hydrogen. It was also known that sodium reacts with alcohols to release $\ce{H2}$. it was concluded that some freshly generated ("nascent") hydrogen was responsible for this remarkable reaction. Subsequent studies have shown that this reaction proceeds via electron-transfer from metallic sodium to the ester substrate followed by protonation of the reduced intermediate. The evolution of hydrogen by the reaction of sodium and alcohol is purely a competitive reaction, the sole benefit being that in the presence of sufficient alkoxide, the sodium/alcohol reaction slows.

So in general, at least toward organic compounds, your relative reactivities of hydrogen species are correct if you take out "nascent" hydrogen so that:

$$\ce{H2} \lt \rm atomic~hydrogen$$

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I wonder why, instead of a vague comment that the book is "not old" (whatever that's supposed to mean), you didn't provide its citation.

I'm familiar with the use of a metal surface to catalyze hydrogenation reactions. I'm not familiar with the concept of "nascent hydrogen". First, an arc discharge can reach temperatures of several thousands of degrees. So, I have to assume that we are not talking about atomic hydrogen at such temperatures, but rather in a highly diluted state in, say STP air. Otherwise a comparison of it with the supposed aqueous species [H] wouldn't be very useful. (Hint: atoms are indeed more reactive at higher temperatures.)

There's another problem which is the metal surface. As I said, I'm familiar with the increased reactivity that H2 shows when absorbed onto a metal surface (also H+) but apparently your textbook is claiming that there exists a species [H] in solution. I need the citations to the primary literature to believe that.

The final problem (and I'm not actually sure the distinction is a difference) is the different states and environments of the species H (gas phase, dilute) with [H]aq. At first, chemistry seems to be about atoms and molecules interacting in simple ways in isolation. It doesn't take long at all, to see that environment matters greatly. I don't understand what the context is for your question. In what context will [H] (if it exists as a separate species, and I'm dubious) be compared to atomic H? Was the atomic H dissolved in water so that the environments were comparable?

One last comment: Climbing the steps of knowledge is hard. If you have taken one step farther than anyone before you, it is a major accomplishment. There are few who are able to take more than a few steps up. Even Einstein failed in his rejection of Quantum Mechanics. My point here is that if your textbook is "new", then how old is its author? Is he (she) possibly stuck with some obsolete paradigms?

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