The most common and most likely answer to this crossword clue is the 7 letter word FALLACY
I've seen this crossword clue in The Guardian
F
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More clues leading to the result FALLACY
Buddy explains!

The straight part
We know that "Unsound notion" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case unsound notion = fallacy.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does FALLACY mean?
FALLACY noun- Deceptive or false appearance; that which misleads the eye or the mind.
- An argument, or apparent argument, which professes to be decisive of the matter at issue, while in reality it is not. A specious argument.